A semi-quantitative x-ray diffraction technique for estimation of smectite, illite, and kaolinite
by Roger W E Hopper
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Soils
Montana State University
© Copyright by Roger W E Hopper (1981)
Abstract:
Two studies are reported.
I. An assessment of the major sources of error in the X-ray diffraction procedure was conducted using a
nested design and ANOVA for peak area and clay mineral composition. Clay separation, slide
preparation and slide positioning were significant sources of error.
II. Modifications of the factor method for semi-quantitative characterization of clay mineral
composition by X-ray diffraction analysis were tested. Samples used in the study were from early
Tertiary aged sediments of the Fort Union Formation and associated soils in Southeastern Montana.
Estimates of the total CEC of the clay-sized fraction were based on X-ray diffraction results. The
accuracy of estimation for each modification was tested by linear regression comparing these estimates
with measured CEC values. Variation in measured CEC explained 90% of the variation in estimated
CEC, 92% of the variation in smectite composition, and 82% of the variation in kaolinite composition.
Percent illite was compared with illite content estimated by total K analysis. Variation in measured
illite content accounted for 74% of the variation in estimated illite content.
A modification of the factor method is presented that provides relatively fast and reasonably accurate
estimations of percent smectite, illite, and kaolinite for material that does not contain significant
portions of vermiculite or chlorite. STATEMENT OF PERMISSION TO COPY
In presenting this thesis in partial fulfillment of the requirements for an advanced
degree at Montana State University, I agree that the Library shall make it freely available
for inspection. I further agree that permission for extensive copying of this thesis for schol­
arly purposes may be granted by my major professor, or, in his absence, by the Director of
Libraries. It is understood that any copying or publication of this thesis for financial gain
shall not be allowed without my written permission.
Signature_________________ „
not*
/W
A SEMI-QUANTITATIVE X-RAY DIFFRACTION TECHNIQUE FOR
ESTIMATION OF SMECTITE, !ELITE, AND KAOLINITE
by
ROGER W E HOPPER
A thesis submitted in partial fulfillment
of the requirements for the degree
of
MASTER OF SCIENCE
in
Soils
Approved:
Chairperson, Gradpdm Committee
Head, Major Department
Graduate Dean
MONTANA STATE UNIVERSITY
Bozeman, Montana
November, 1981
iii
ACKNOWLEDGMENT
The author wishes to express his gratitude to Dr. Murray G. Klages for providing:
suggestions, constructive criticism, and unfailing patience and support during the extended
time taken to complete this thesis.
In addition, appreciation is extended to Dr. Hayden Ferguson, Dr. Gerald Nielsen,
and Dr. Theodore Weaver for serving on the author’s graduate committee, for providing
needed assistance and for providing clear insights into the complicated interactions of our
natural environment.
The friendships made while at Montana State University helped create the perfect
atmosphere in which to study and work.
Finally, I must thank my wife, Glenna. Over the past four years she provided the
best combination of patience, support, logic and cajolery without which I might never have
completed this thesis.
I
TABLE OF CONTENTS
Page
VITA............................................. ............................................... ..................................
ii
ACKNOWLEDGMENT............................................................................................. i ..........
iu
TABLE OF CONTENTS......................................... ! ............................................................
iv
LIST OF TABLES............................................................................................................ ...... vi
LIST OF FIGURES.............................. .......... ....................... ! .................................... .. . . ;
ix
ABSTRACT..........................................................
INTRODUCTION...................................................... ..........................................................,
x
I
MATERIALS AND METHODS --MAIN STUDY........... ...........................................
Samples............................
Sample Preparation........................; ................... ..................................................... ....
Total Potassium Determination..........................
Cation Exchange Capacity Determination...................
X-ray Diffraction Analysis. ;■......................................................................................
Cation Exchange Capacity Estimation.................................... ....................................
Statistical Methods .............................................. .............................................
m cn vi l>
LITERATURE REVIEW..................................... ............./.
Sample Dispersion and Particle Size Segregation . . . . .
Sample Preparation and Presentation........................
Quantitative Estimation of Clay Mineral Components,
12
12
12
13
14
14
19.
20
MATERIALS AND METHODS-PRELIMINARY STUDY............. ..................... ............ 21
RESULTS AND DISCUSSION............................................................ : ..............................23
I. Preliminary Study—Sources of Error in Laboratory Technique........................... 23
Significant Main Effects in Determining Peak Area Over All
Soils T e sted ................................ ........................... .............................. .............. 25Sources of Error in Determining Clay Mineral Composition
Between Soils................................. ..................................................................... 26
. II. Main Study—Quantification
............................................................................28
Cation Exchange Capacity Estimation......................................... .................
28
Smectite E stim ation........................................... ............................................. . . . 3 6
V
Page
Illite E stim ation........................................................
.4 2
Models derived assuming 8.3% elemental K per unit cell illite ........................ 43
Models derived assuming 5.1% elemental K per unit cell illite ........................47
Kaolinite Estimation............................................................................................. : 51
SUMMARY AND CONCLUSIONS................................
57
LITERATURE C ITE D ............................................................................................................. 61
APPENDIX
67
vi
LIST OF TABLES
Table
Page
1. Sample Identification and D escription................. ................................................... 13
2. Percent of Total Variance for Main Effects on Peak Area for All
Soils Studied................................................................................................................... 24
3. Percent of Total Variance for Main Effects on the Determination
of Clay Mineral Composition Over All Soils Studied................................................37
4. Linear Regression Models of the Measured CEC on Estimated CEC ...................... 28.
5. Selected Linear Regression Models of Measured CEC on Estimated
CEC.....................................................................
29
6. Selected Linear Regression Models of Estimated CEC on Measured
CEC...........................................................................................................................
32
7. Selected Linear Regression Models of Estimated Smectite Content
on Measured Cation Exchange C apacity......................................................................36
8. Selected Linear Regression Models of the Difference in Estimated
and Measured Cation Exchange Capacity on Estimated Smectite
Content............................................................................................................................ 40
9. Selected Linear Regression Models of Estimated Illite Content on
Measured Illite Content on Measured Illite Content (Assuming
8.3% K per Unit Cell Illite). . . . ; ......................................... .................................... 43
10. Selected Linear Regression Models of Estimated Illite Content on
Measured Illite Content (Assuming 5.1% K per Unit Cell Illite).................................47
11. Selected Linear Regression Models of the Difference in Estimated
and Measured Illite Contents on Estimated Illite Content (Assuming
8.3% K per Unit Cell Illite) ................................
48
12. Selected Linear Regression Models of Estimated Kaolinite Content
on Measured Cation Exchange C apacity..................................................................... 51
13. Selected Linear Regression Models of the Difference in Estimated
and Measured Cation Exchange Capacity on Estimated Kaolinite
Content...............................................................
53
vii
Table
Page
14. ANOVA Tablfe (Over All Thr^e Soils T e ste d )...........................................................68
15. Peak Area Measurements (in2) for the Preliminary Study....................................... 69
16. Percent Clay Mineral Composition for the Preliminary Study. . . .......................... 75
17. ANOVA for Main Effects on the 17A Peak (MgEG) for All Three
Soils Studied—Preliminary Study . . .............................................................................82
18. ANOVA for Main Effects on the I OA Peak (MgEG) for All Three
Soils Studied-Preliminary S tu d y .................................................................
82
19. ANOVA for Main Effects on the 14A Peak (MgEG) for All Three
Soils Studied—Preliminary S tu d y .....................
83
20. ANOVA for Main Effects on the 14A Peak (K350) for All Three
Soils Studied—Preliminary S tu d y ...............
83
21. ANOVA for Main Effects on the 7A Peak (MgEG) for All Three
Soils Studied—Preliminary S tu d y ...............
84
22. ANOVA for Main Effects on the 7A Peak (K350) for All Three
Soils Studied—Preliminary S tu d y .................................................
84
23. ANOVA for Main Effects on the 3.5A Peak (MgEG) for All Soils
Studied—Preliminary Study........................................................................................... 85
24. ANOVA for Main Effects on the 3.3A Peak (MgEG) for All Three
Soils Studied—Preliminary S tu d y .....................
85
25. ANOVA of Percent Smectite Composition for All Three Soils
Studied—Preliminary Study......................................................
86
26. ANOVA of Percent Illite Composition for All Three Soils Studied
-Preliminary Study........... .................................................
86
27. ANOVA of Percent Vermiculite Composition for All Three Soils
Studied—Preliminary Study..........................................................
87
28. ANOVA of Percent Chlorite Composition for All Three Soils
Studied-Preliminary Study...................
87
29. ANOVA of Percent Kaolinite Composition for All Three Soils
Studied—Preliminary Study............................................................ : ..........................88
viii
Table
Page
30. ANOVA of Percent Quartz Composition for All Soils Studied
—Preliminary Study................................................
88
31. Complete Area Measurements (in2) for thd Main S tu d y ...................................
89
32. Complete Data Table for Modification IV ...........................................................
93
33: . Complete Data Table for Modification V ....................................... ......................... 95
34. Complete Data Table for Modification IX ..................................................; .............97
35. Complete Data Table for Modification X ........... ........................................................ 99
ix
LIST OF FIGURES
Figure
Page
1. Peak Area Determination . .......................................................................................... 18
2. Linear Regression Model of Measured CEC on Estimated CEC for
Modification X .................................................................................................... ..
31
3. Linear Regression Model of Estimated CEC on Measured CEC for
Modification X .........................................
34
4. Linear Regression Model of Estimated Smectite Content on
Measured Cation Exchange Capacity..........................
37
5. Linear Regression Model of the Difference in Estimated and
Measured Cation Exchange Capacity on Estimated Smectite
Content.................................................................
41
6. Linear Regression Model of Estimated Illite Content on Measured
Illite Content (8.3% K) for Modification V ................................................................. 45
7. Linear Regression Model of Estimated Illite Content on Measured
Illite Content (8.3% K) for Modification X ...............................................................46
8. Linear Regression Model of the Difference in Estimated and
Measured Illite Content on Estimated Illite Content (assuming
8.3% K per unit cell illite)..............................................................................................50
9. Linear Regression Model of Estimated Kaolinite Content of
Measured Cation Exchange Capacity...........................................
54
10. Linear Regression Model of the Difference in Estimated and
Measured Cation Exchange Capacity on Estimated Kaolinite
Content...................................................................................; .................................... 56
ABSTRACT
Two studies are reported.
I. An assessment of the major sources of error in the X-ray diffraction procedure
was conducted using a nested design and ANOVA for peak area and clay mineral compo­
sition. Clay separation, slide preparation and slide positioning were significant sources of
error.
II.
Modifications of the factor method for semi-quantitative characterization of
clay mineral composition by X-ray diffraction analysis were tested. Samples used in the
study were from early Tertiary aged sediments of the Fort Union Formation and asso­
ciated soils in Southeastern Montana. Estimates of the total CEC of the clay-sized fraction
were based on X-ray diffraction results. The accuracy of estimation for each modification
was tested by linear regression comparing these estimates with measured CEC values. Vari­
ation in measured CEC explained 90% of the variation in estimated CEC, 92% of the vari­
ation in smectite composition, and 82% of the variation in kaolihite composition. Percent
illite was compared with illite content estimated by total K analysis. Variation in measured
illite content accounted for 74% of the variation in estimated illite content.
A modification of the factor method is presented that provides relatively fast and
reasonably accurate estimations of percent smectite, illite, and kaolinite for material that
does not contain significant portions of vermiculite or chlorite.
INTRODUCTION
X-ray diffraction methods are central to studies of the clay fraction of soils with
the exception of those soils suspected to contain large amounts of amorphous material. A
study of the components of the clay fraction of soil must begin with the proper identifi­
cation of the minerals present. Quantitative estimations of the clay mineral components
have applications to many disciplines.
Several methods have been employed to make quantitative estimations of clay
minerals in soil investigations. The factor method used in making the investigations reported
here has the advantages of being relatively rapid and precise. However, estimations obtained
are relative values. Consequently, the method has been referred to as semi-quantitative.
Few investigations report tests of the accuracy of quantitative estimations. McNeal [31]
used a combination of chemical and X-ray diffraction methods to make quantitative esti­
mations of the mineralogy of arid and semi-arid land soils.
The objective of this study was to derive a relatively fast and reasonably accurate
method of determining clay mineral composition of soils and associated parent material for
application to large numbers of samples. Ten modifications of the factor method for semiquantitative characterization of clay mineral composition by X-ray diffraction analysis
were tested for accuracy and precision. Appropriate factors were determined. Estimations
of relative mineral composition and cation exchange capacity derived from X-ray diffraction
results were tested against cation exchange capacity values obtained by chemical methods.
Estimates of the percent illite derived from X-ray diffraction analysis were tested against
percent illite values obtained from total potassium analysis.
2
In addition an attempt was made to assess the major sources of error in the method
of X-ray diffraction analysis used in this study, and to identify the diffraction maxima that
may be measured with the greatest precision.
LITERATURE REVIEW
Quantitative applications are firmly based on sound theoretical considerations.
However, almost every procedural step in X-ray diffraction methods may be considered as
a potential source of error [16,43,32,39]. In this review of pertinent literature, an attempt
is made to briefly survey the major procedural steps in making quantitative clay mineral
estimations by X-ray diffraction methods. These steps may be identified as: (I) sample dis­
persion and particle size segregation, (2) sample preparation and presentation, and (3)
quantitative estimation of clay mineral components.
Sample Disperson and Particle Size Segregation
Day [7], Kunze [27], Kittrick and Hope [23], Jackson [18] and Watson [53]
provide reviews of procedures applicable to sample dispersion. It is generally accepted that
cementing agents and free oxides and salts should be removed to some extent to aid in dis­
persion. Apparent disagreement does exist, however, as to the severity of the pretreatment
required.
The procedures described by Jackson [18] are generally rigorous. It has been
demonstrated that less severe pretreatments are adequate to obtain satisfactory sample dis­
persion and X-ray diffraction results [23]. Several authors have found that sample pretreat­
ment can seriously affect apparent clay mineral composition. Harward, Theisen, and Evans
[17] compared the effects of several different dispersion methods. Generally, they found
that, although iron removal enhanced dispersion, it also resulted in significant differences
in apparent clay mineral composition. More rigorous iron removal and dispersion treatments
generally resulted in a greater number of clay minerals identified, however, this was also
dependent upon the soil itself.
4
The choice of the proper combination of pretreatment and dispersion methods
remains to the discretion of the investigator. A combination of methods might be most
worthwhile. While it is important to identify the maximum number of mineral components
present, it is also advantageous to use those methods which retain the real mineral as­
semblages as they exist in situ [17].
Use of ultrasonic vibrations to obtain sample dispersion may eliminate need for
drastic pretreatment. Olmstead [37] found that sonic vibrations could be used in con­
junction with chemical treatments to obtain stable dispersed suspensions of soil colloids.
However, his work was largely overlooked for almost thirty years. Recently Edwards and
Bremner [9,8] found, using soils having a wide range of characteristics, that sample dis­
persion could be obtained with most soils using only distilled water, thus reducing both the
time involved in treating the sample and the possibility of destruction of natural mineral
structure. This work has been corroborated by Genrich and Bremner [12]. Vladimirov [52]
suggested the value of ultrasonic dispersion methods in studying highly calcareous soils
where chemical treatments disallow a particle size investigation of carbonate salts. Emerson
[10] found that sodium hexametaphosphate improved dispersion of soils particularly high
in organic matter or soluble salts. In most cases it has been reported that abrasion of miner­
als is lower using ultrasonic methods than with either shaker or mixer methods of mechani­
cal dispersion except in the case of biotite [9].
Particle size segregation may be obtained by settling or centrifugation [18]. Tan­
ner and Jackson [48], in considering settling and centrifugation techniques, have pub­
lished nomographs by which the sedimentation of particles having a particular effective
radius may be predicted according to time temperature, particle density and centrifuge
5
speed. Procedures employing density gradient centrifugation and heavy liquid techniques
have not received much attention in clay mineralogy as yet. Towe [51] suggested these
latter techniques while critically considering the use of the less-than-2-micron particle size
fraction in making typical clay mineral studies. Towe seriously questioned the ability of
current sedimentation and centrifuge techniques to yield accurate representative samples
of this size fraction based on inherent differences in particle density and settling times.
Sample Preparation and Presentation
Preferential orientation is rather easily obtained because of the shape of most
layer-silicate minerals. Orientation results in the enhancement of basal (OOl) diffraction
maxima and thus permits greater sensitivity to small amounts of the mineral components
present [27].
The length of the specimen irradiated and the depth to which the X-ray beam pene­
trates are functions of the angle at which the X-ray beam intersects with the sample (0).
The length of the irradiated specimen (L) may be calculated by the relationship:
L = aR/2sin0 ,
where a represents the divergence slit width (in radians) and R represents the radius of the
goniometer [38]. The irradiated specimen length increases rapidly at smaller angles of 0.
This results in a maximum d-spacing that may accurately be measured and a minimum
sample length. It is interesting to note that the majority of studies reported in the litera­
ture use CuKa radiation in conjunction with a divergence slit width of 1° to study soil clay
minerals. According to the values reported by Parrish [38] the maximum d-spacing accu­
rately measured under these conditions is 5.2A, a value well below even the relatively small
c dimension of the kaolinite minerals (approximately I A).
6
Cullity [6, pp. 269-272] described the effective depth of X-ray penetration in terms
of the fraction (Gx) of the total diffracted intensity contributed by a surface layer of a
certain thickness (x) by the relationship:
Gx = ( I - B - 2^xZsine) ,
where ju represents an appropriate mass absorption coefficient. Gibbs [13] used this
equation to calculate penetration values. The need for a uniform sample in which no parti­
cle segregation has occurred is imperative.
In a comparison of several techniques Gibbs [13] found that particle segregation
was best avoided by smear-on-glass techniques as described by Theiseri and Harward [50]
and suction-on-ceramic tile techniques described by Kinter and Diamond [22]. Centrifuge
methods for deposition on either ceramic tiles or glass were found to cause particle size
segregation and thus bias estimates toward the finer grained smectite minerals.
An additional consideration in preparing oriented samples is the degree of orien­
tation that is actually achieved. Departure from the preferred orientation can cause a
reduction in the peak interisity. Taylor and Norrish [49], using the suction-on-ceramic tile
method reported significant variations in the degree of preferred orientation between
specific minerals. They also found that variations in the degree of orientation for specific
minerals may vary between duplicates. Quakemaat [41] reported relatively low absolute
orientation for all minerals studied using a suction-on-plastic membrane technique.
Schultz [44], in a study of kaolinite-illite mixtures using a smear-on-glass technique,
found that the degree of preferred orientation in pure kaolinite samples, was greater than
the orientation of either kaolinite or illite in mixed samples. However, for any one mixture,
7
the preferred orientation of the kaolinite and illite was about the same. He concluded that
the effect of orientation was eliminated within a single slide.
At present no clear advantage is held by either the smear-on-glass or the suction-onceramic tile techniques in !comparison with each other [50].
Quantitative Estimation of Clay Mineral Components
Quantitative X-ray diffraction methods fall into three basic approaches described
here as: (I) the Theoretical Method, (2) the Standard Clay Mixture Methods, and (3) the
Factor Method.
The Theoretical Method. The work reported by Alexander and Klug and their
associates [1,24,25] form the theoretical basis for current quantitative methods. In its
simplest form, the method of Alexander and Klug [ I ] reduces to:
V 1OjP s wP ’
where Ip equals the diffraction intensity of the P component iri a multiphase mixture, I q p
equals the diffraction intensity of the P component in pure form (the external standard),
and Wp equals the weight fraction of the P component in the mixture. This method assumes
that the mass absorption coefficient of the P component (ju*p) is equal to the mass absorp­
tion coefficient of the matrix containing the rest of the components of the mixture (#*%).
This assumption is not strictly true and can lead to large errors. Leroux, Lennox, and Kay
[28] attempted to correct for this by extending Eq. I to include a ratio of the mass
absorption coefficient of the P component to the average mass absorption coefficient of
the mixture (ju ^1):
.
V 1OjP= wP0V ^ -
8
Tabulated values of m* for several minerals are available [3]. Assuming an investigator has
previously determined I q p, the application of this technique requires only a measurement
of Ip and
Williams [57] provided an improved method for determining the average
mass absorption coefficient.
The Standard Clay Mixtures Method. Methods using mixtures of standard clays
have been applied through two basic avenues for quantification: (I) the calibration curve
approach and (2) the empirical factor approach.
The calibration curve approach uses mixtures of known weighed amounts of stand­
ard clay minerals to calibrate the method. Probably the most extensive use of this tech­
nique was that of Willis, Pennington, and Jackson [58]. They used 141 standard clay mix­
tures containing either 2, 3, 4, 5, or 6 components based on their conception oLthe
weathering sequence of clay size material. Talvenheimo and White [47] used a diffractome­
ter in developing a standard clay mixture method for multiphase system containing kaolinite, illite, and bentonite. With this technique they reported 5 to 10% accuracy.
Internal standards have been employed in the calibration curve approach. Com­
pounds such as MgO, LiF, and CaF2 having low absorption coefficients and high sym­
metry are normally used [3] so that small amounts may be incorporated in the sample
to be measured without disrupting the desired degree of orientation. The internal stand­
ard method of quantitative analysis is based upon the ratio of the integrated intensity of
a component in a clay mixture with the integrated intensity of an internal standard added
to the mixture in a constant amount. Calibration curves are normally prepared using syn­
thetic mixtures of standard clay samples together with a constant amount of the internal
standard. The use of an internal standard circumvents the need to know mass absorption
9
coefficients or crystal lattice parameters. Because of this advantage the method has been
applied to the study of soil clays by several investigators. Many of these investigations were
done using photographic techniques on random powder mounts [55,19]. In a more recent
study, Glenn and Handy [15] applied the internal standard method using a diffractometer.
Orientation problems have been approached by Quakernaat [41] by the use of
molybdenite as an orientation indicator. Compensating for deviations from preferred
orientation, he set up quantity intervals using standard mineral mixtures. In determining
quantities of kaolinite, illite, and smectite, he claimed an accuracy of about 7 percent.
Estimations of chlorite, vermiculite, an d . pyrophyllite were within about 10 percent
accuracy.
The empirical factor approach is best exemplified by the work of Schultz [44,45].
Basically this method uses standard clay minerals in binary combinations to obtain ratios
of integrated diffraction intensities for two minerals. These ratios were than applied to a
multiphase mixture, to characterize the peak intensities to obtain relative clay mineral com­
positions. As stated previously, Schultz recognized that such factors not only resulted from
characteristics of the composition and lattice structure of the minerals, but from orientation
effects as well. Schultz reported that in 50/50 mixtures by weight of several kaOlinites to
Fithian Illite, the ratio of the integrated intensities was approximately 1/1. He found no
consistent ratio for chlorite minerals. In a similar study Moore [33] reported the accuracy
to be within 2 percent of the actual values.
The major problem shared by the methods employing mixtures of standard clays
is the difficulty faced in obtaining mineral standards that are comparable to the clays
naturally occurring in soils. Gibbs [14], however, has reported a ,technique in which he
10
obtained standard minerals directly from the samples to be studied. Coupling the approach
of Schultz as described above together with an internal standard method, he avoided the
problems of absorption and crystallinity differences between the standards and the
unknowns.
The Factor Method. The factor method incorporates the use of an empirical multi­
plication factor by which measured peak intensities or integrated intensities are character­
ized. These factors may be derived experimentally as in the case of studies reported by
Weaver [54] and Freas [11], or by calculations based on chemical and crystal lattice
parameters [4,42]. The method has several advantages in that it is relatively rapid and
generally has good precision. Any of the diffraction maxima may be used in the calcu­
lations along with a careful and reasonable choice of multiplication factors.
The method as outlined by Johns, Grim, and Bradley [20] is probably the most
often cited of all quantitative procedures. Basically it uses illite somewhat like an internal
standard. The integrated intensities of the diffraction maxima of the other minerals are
then related to the integrated intensity of the illite peak by appropriate multiplication
factors. They used two illite peaks for comparison purposes. The IOA illite peak was multi­
plied by 4 to allow direct comparison with the 17A peak of smectite. The 3.3A peak was
compared directly with the 3.5A maximum for chlorite and kaolinite. Heat treatments
were used to discern minerals which occur concurrently in a peak. An apparently arbi­
trary correction for quartz was applied with the 3.3A peak of illite.
Similar applications of this method have been reported by several authors and dif­
fer from the method of Johns et al. by either the method used to determine peak intensity
11
or integrated intensity, in the multiplication factors used, and/or in the diffraction maxima
being measured. Weaver [54] used a factor of 2.5 in comparing the 7A peak with the IOA
peak for the determination of kaolinite. Freas [11], on the other hand, in comparing all
minerals present to the (001) diffraction maximum of kaolinite at 7A, used factors of 3, 3,
and I for comparison with the (001) reflections of iltite, chlorite, and smectite, respec­
tively. Biscayne [2] in comparing all minerals to the 17A peak of montmorillonite used a
factor of 4 for the 10A peak of illite and a factor of 2 for a comparison with the 7A peak.
The relative composition of chlorite and kaolinite was further discerned by using the
doublet occurring near 3.5A. Meade [29] assumed that smeptite, Jcaolinite, and illite
reflected X-rays at the same intensity. In addition, he used different intensity factors for
Type A chlorite (x2) and Type B chlorite (x 1.5) at 7A for comparison with the 10A peak
of illite. The method of Keller and Richards [21] is closely similar to that of Johns et al.
with the exception that a factor of 3 was used to compare the 17A peak to the 10A peak.
Npiheisel and Weaver [34] used a factor of 2 for comparing the 17A and 7A peaks with
the 10A peak.
MATERIALS AND METHODS
MAIN STUDY-QUANTIFICATION
Samples
The fifty samples used in this study were obtained from the Decker Coal Company,
Decker, Montana. The material consists of early Tertiary aged sediments of the Fort Union
Formation, together with soil formed on this moderately indurated material.
The samples were chosen on the basis of clay mineral composition estimated from
preliminary X-ray diffraction analysis in an effort to obtain a wide range of clay mineral
composition. The description of those samples used in this study appeared in Table I.
Sample Preparation
The samples were first ground to pass a 2mm sieve. Sample dispersion was obtained
by using a probe-type ultrasound machine (120 volts, 4 amps, 60 cycles) manufactured by
Blackstone Ultrasonics, Inc. Ten grams of each sample were placed in 50 ml of 0.01%
Na3CO3 and subjected to ultrasound for 2 minutes. Excessive heating of the samples was
experienced using longer periods of dispersion.
Stock clay-sized (< 2p) particle suspensions were prepared for each sample by five
washings using 0.01% Na2CO3, centrifuging at 500 RPM according to the nomographs of
Tanner and Jackson [48], and saving the supernatant from each wash. Four 25 ml sub­
samples were removed from these stock suspensions and prepared for X-ray diffraction
analysis as described below. The remaining stock suspensions were saturated with calcium
by centrifuge washing three times with N CaCl2. Excess salt was removed by simple dialy­
sis until a test for chloride was negative. Upon completion of dialysis the samples were air
dried and hand ground with an agate mortar and pestle to pass a 60 mesh sieve.
13
Table I . Sample Identification and Description
Sample No.
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
.
Description
(Depth in
Feet)
Lab.
Ident. No.
44518
44519
44520
44521
. ,44522
44523
44524
44525
44528
44529
44530
44531
44532
. 45245
45246
45247
45248
45249
45250
45251
45252
45253
45254
45255
45256
.
0 -2
2 -5
5-11
11-15
15 -20
20-23
23 - 27
27-29
.
40-45
45-50
. 50-55
55-60
60-65
0 -2
2 -5
5-11
11 -15
15 -20
20-25
25-28
28-34
34-40
40-44
44-49
49 - 54
Sample No.
Lab.
Ident. No.
Description
(Depth in
Feet)
26
27 .
28 .
29
30
31
32
33
34
35
36
37
38 ..
39
40
41
42 ■
43
44
45
46
47
48
49
50
45257
45258
45261
45262
45263
45264
1235-4
1235-5
1235-6
1235-8
1235-9
1235-10
1237-1
1237-2
1237-3
1237-4
1237-5
1237-6
1237-8
1237-10
1237-11
1237-12
1237-13
1256-2
1256-12
54-60
60-65
75-77
129-135
135-140
140 -145
55-60
60 - 66
73-78
103-107
107-117
117-126
5 -1 0
10-20
20-25
25-35
35 -45.
45-50
60-70
98.8 -105.3
105.3-110.0
111.8-120
120-130
42-52
138-142
Total Potassium Determination
Duplicate 0.0500 g clay samples were weighed. The HFrHClO4 decomposition
method was employed as suggested by Pratt [40]. The extract was diluted to lOO ml. so
that the resulting solution contained 0.5% Sr as SrCl2. The concentration of potassium
ions in solution was determined by atomic absorption. The results were reported in terms
of illite, expressed as a percentage of the total clay fraction as calculated assuming 8.3%
14
[30] and 5.1% [54] elemental potassium per unit cell illite. The resulting estimations of
the percent illite were tested against the percent illite estimated by X-ray diffraction analy­
sis using linear regression methods.
Cation Exchange Capacity Determination
Free carbonates were removed from the dry Ca-saturated clay samples by a modifi­
cation of the method described by Jackson [18]. The modification involved four centri­
fuge washings with normal sodium acetate buffer (pH 5.0) without heating the sample.
Following carbonate removal air-dried Ca-saturated clay samples were prepared by the
method previously described.
The cation exchange capabilities of the clay samples were determined by a Ca//Mg
exchange system. Duplicate 0.050 g samples were centrifuge washed four times using
10 ml aliquots of N MgCl2, saving the supernatant following each wash. The resulting
extract was diluted to 50 ml so that the resulting solution additionally contained 0.5% Sr
as SrCl2. The concentration, of Ca in the extract was determined by atomic absorption and
the results reported in terms of m eq/100 gm of clay.
X-ray Diffraction Analysis
One subsample of each clay sample was saturated with Mg by centrifuge washing
three times with 25 ini aliquots of N MgCl2. Excess salt was removed by washing twice
with distilled water. A second subsample was saturated similarly with potassium using
N KC1. Excess salt was removed by washing, once with distilled water followed by a second
wash with 50% ethanol. SybsampIes were duplicated for each clay sample.
15
Parallel oriented samples were prepared by the paste method of Theisen and Harward [50]. The Mg-saturated samples were ethylene glycol solvated by the condensation
method described by Kunze [26]. K-saturated samples were heated to both 350°C and
550° C for three hour periods.
X-ray diffraction analysis was carried out on a General Electric XRD-5 diffractome­
ter using Ni filtered CuKa radiation at 45Kv and 18ma with beam and detector slit widths
of 1° and 0.2°, respectively. Medium range collimating assemblies were used for both the
incident and reflected beams. Scanning speed of the goniometer was 2° 20 per minute and
the chart speed was I inch per minute, giving a 2° 26 per inch diffractogram scale for all
samples. All Mg-saturated, ethylene glycol solvated samples were scanned through a 20
range of 2°-30°. A 2°-15° 20 range was used for K-saturated samples for both heat treat­
ments.
The criteria used to identify the clay minerals present in the samples were taken
from [18], [56], and [5] and are as follows:
Mineral Group
Identification Characteristics
Smectite
d(001) maximum at approximately 17A
under Mg-saturation and glycol solvation. Ksaturation together with heat treatments
cause progressive collapse of interlayer space
resulting in a d(001) maximum at approxi­
mately IOA for the K-saturated, 550°C heat
treatment.
16
Vermiculite
d(001) maximum
at approximately 14A
under Mg-saturatioh and ethylene glycol sol­
vation. Total collapse of the interlayer space
and a consequent d(001) maximum of ap­
proximately IOA result from K-saturation to­
gether with heat treatments. .
Chlorite
d (001) maximum at approximately 14A for
all treatments, d (002) maximum may or may
not be present in the K-saturated, 550°C heat
treatment.
Illite
d(001) maximum at approximately 10A for
all treatments.
Kaolinite
d (001) maximum at approximately 7A and a
d(002) maximum at 3.SA for all treatments
except K-saturated, SSO0C heat treated sam­
ples. On heating to approximately SSO0C the
mineral reported here as kaolinite becomes
amorphous to X-rays due to the collapse of
crystalline structure.
Quartz
a diffraction maximum at approximately
3,3A and coincides with an accompanying .
id(003) maximum of illite.
\
17Peak intensities of the d(001) reflections were measured to a hand-drawn back­
ground line. The areas under the peaks were estimated by multiplying the peak height by
the width of the peak at half the peak height [36], as illustrated in Fig. I.
Characterization of the minerals followed the factor method of Johns, Grim, and
Bradley [20] as modified by Wilding [59]. Modifications in.this method involved both the
peaks and factors used to characterize the minerals considered. First order basal reflections
were used in the characterization of all clay minerals. The 3.3A reflection was used to
characterize quartz. Often the 14A peak of the Mg-saturated, ethylene glycolated slide ap­
pears as a shoulder on the high angle side of the 17A peak. In such cases the low angle side
of the 14A peak was estimated, as in Fig. I, and the area calculated. The area of the'TVA
peak was then corrected by subtracting the area of the 14A peak from the area of the 17A
peak.
Teh modifications were tested involving different factors for smectite and kaolinite.
Computer programs were used to complete the characterization. The following compu­
tations were used to calculate characterized peak areas:
Modification I.
17A Mg-sat. E.G./4
= Smec. Peak Area
(14A Mg-sat. E.G. minus 14A K-sat. 350°C)/2
= Verm. Peak Area
14A K-sat. 350"C/2
= Chlor. Peak Area
IOA Mg-sat. E.G./1
= 111. Peak Area
(7A Mg-sat. E.G. minus 7A K-sat. 550°C)/4
=? Kaol. Peak Area
(3.3A Mg-sat. E.G. minus 3/4(10A Mg-sat. E.G.j/4
= Quar. Peak Area
18
Figure I . Peak Area Determination
A=
B=
C =
II =
W=
Hand drawn background line
Hand drawn line estimating the extent of the peak
Area of peak overlap
Maximum height of peak measured from A
Peak width measured at 11/2
Peak Area = H x W
19
Modifications II, III, IV, and V were similar to Modification I except that the (7A
Mg-sat. E.G. minus I A K-sat. 550°C )peak area was divided by 3, 2.5, 2, and I, respectively,
for kaolinite estimates. Modifications VI, VII, VIII, IX, and X were similar to Modifi­
cations I-V except that the 17A Mg-sat. E.G. peak area was divided by 5 for smectite esti­
mates.
For each modification tested, the characterized peak areas were totaled and the
relative percent composition of each mineral calculated according:
Smec. Pk. + Verm. Pk. Area + Chlor. Pk. Area
+ Kaol. Pk. Area + Quar. Pk. Area = Total Peak Area
Percent Smectite = Smec. Pk. Afea/Total Pk. Area X 100
Percent Vermiculite = Verm. Pk. Area/Total Pk. Area X 100
Percent Chlorite = Chlor. Pk. Area/Total Pk. Area X 100
Percent Illite = 111. Pk. Area/Total Pk. Area X 100
Percent Kaolinite.= Kaol. Pk. Area/Total Pk. Area X 100
Percent Quartz = Quar. Pk. Area/Total Pk. Area X 100
Cation Exchange Capacity Estimation
Cation exchange capacity values were estimated for the < 2p particle size fraction
of each sample by multiplying the percent mineral compositions estimated by each modi­
fication with cation exchange capacity values reported by McNeal [31] for the minerals
considered:
Smectite
Illite
Kaolinite
Chlorite
Vermiculite
Quartz
100 meq/100 g
25 meq/100 g
. 8 m eq/100 g
25 meq/100 g
175 meq/100 g
2 meq/100 g
20
The resulting estimated cation exchange capacity values were tested against the
cation exchange capacity values determined by the laboratory procedure previously
described, using linear regression methods.
Statistical Methods
Correlations were computed using, the Bivariate Correlation Analysis routine, sub­
program Scattergram and the Multiple Regression routine, subprogram Regression of the
Statistical Package for the Social Sciences [35]. For each modification, linear regression
models were developed for the following:.
dependent
MCEC
ECEC
ESM
ECDIF
EIL
EIL
ILDIFB
EKA
ECDlF
vs.
where,
ECEC
MILS
MILS
EIL
ESM ,
:
,
,
MCEG
independent .
ECEC
MCEC
MCEC
ESM
MILS
MILS
EIL
MCEC
EKA
'
.
= Cation exchange capacity determined by chemical means: measured
CEC. '
'
= Cation exchange capacity estimated from X-ray diffraction results.
= Relative Illite content of the clay fraction as determined by total potas­
sium analysis assuming 8.3% K per unit cell of IIlite; measured illife
content. .
= Relative Illite content of the clay fraction as determined by total potas­
sium analysis assuming 5.1% K per unit cell of Illite; measured illite
content.
= Percent Illite content of the clay fraction estimated from X-ray diffraction results.
. = Percent Smectite content of the clay fraction estimated from X-fay diffraction results.
_
u
’
'
21
EKA
= Percent Kaolinite content of the clay fraction estimated from X-ray dif­
fraction results.
ECDIF = Difference in CEC of ECEC minus MCEC
ILDIF8 = Difference in the percent Illite content given by EIL minus MILS.
The estimating accuracy and precision of a modification in the factor method was
primarily based on comparisons of the slope, the y-intercept, the correlation coefficient (r),
the coefficient of determination (r2), and the standard error of the estimate (SEE) for the
linear regression models listed above.
PRELIMINARY STUDY-SOURCES OF ERROR
IN LABORATORY TECHNIQUE
Three soils were chosen from samples obtained from the Decker Coal Company,
Decker, Montana, and the Coal Mine Reclamation Program, Montana State University, on
the basis of their relative smectite content:
Ident. No.
SoilA
(High)
Soil B
(None)
Soil C
(low to moderate)
Description
44523
20-30 feet
44531
55-60 feet
15
Colstrip—C.M.
Watershed #1
From each soil, three 10 g samples were taken and clay size (< 2//) material sepa­
rated by the method previously described. From the resulting stock clay suspensions three
Mg-saturated slides and three K-saturated slides were prepared. The Mg-saturated slides
were ethylene glycolated and scanned through a range of 2°-30°, 29. K-saturated slides
underwent successive heat treatments of 350°C and 550°C and were scanned through a
range of 20-15°, 20 following each heat treatment. Each slide was positioned to create
three arbitrary fields on the slide corresponding to center, slightly left of center, and
22
slightly right of center. Three readings were made at each position. The design results in
81 samples from each soil and 243 samples for the whole experiment.
Characterization and relative clay mineral composition were determined by Modi­
fication No. I described previously in Materials and Methods-Main Study.
One-way analysis of variance for the nested design [46] was computed over all soils
tested considering peak area (measured in square inches), and relative clay mineral compo­
sition.
In the analysis Of peak area the following peaks were considered:
Mg-E.G. treatment: 17A, 14A, 10A, 7A, 3.5A, 3.3A
K-35d°C treatment: 14A, 7A
K-550°C treatment: 7A
These peaks have been used in the past by numerous investigators in making quantitative
estimations of clay mineral composition.
RESULTS AND DISCUSSION
The results herein reported and discussed were derived from two separate studies.
The two studies are reported separately under the headings: I. Preliminary Study-Sources
of Error in Laboratory Technique, and II. Main Study-Quantification.
I. PRELIMINARY STUDY-SOURCES OF ERROR
IN LABORATORY TECHNIQUE
Peak area measurements (in2 ) and percent clay mineral composition data appear in
Tables 15 and 16, respectively. Analysis of variance was conducted according to the
model of ANOVA table appearing in Table 14 by computer. Computations were con­
ducted by Dr. Erwin Smith. Complete analysis of variance statistics for peak area appear
in Tables 17-24. Complete analysis of variance statistics for relative percent composition
appear in Tables 25-30.
Percent of the total variance for the main effects was calculated from variance
components' for all analyses and appear in Table 2.
1Variance Components were calculated for the Analysis over all soils by:
^BcA
~ M^soils
- M.^clay sep /b ccln
^CcB
~ ^ c la y s e p . ~ ^ s l i d e / C(^n
8DcC
= MSslide
s N cD
- A field/slide -
S2
- MSreacJ
" MSfield/slide/dn
,
Total Variance = S2 + S^jc Q + Sq g c
sCeB+ s BeA
-
Table 2. Percent o f Total Variance for Main Effects on Peak Area for All Soils Studied
Treatment
Peak
MgEG
17A
Mg EG
14A
MgEG
10A
MgEG
7A
Mg EG
3.5A
Mg EG
3.3A
K350 .
14A
Soil
90.38*
42.46*
81.79*
65.62*
65.98*
62.26*
11.78*
45.74*
Clay Sep./Soil
0.00
7.52*
1.59 .
Slide/Clay Sep.
0.00
0.00
0.00
Field/Slide
8.69*
36.49*
Read/Field
0.92
13.57
.
K350
7A
0.00
6.33 '
0.00
25.06*
14.96*
14.20*
9.66*
0.00
2.45
11.98*
13.04*
13.36*
18.22*
75.88*
26.30*
4.64
3.49
6.47
3.53
12.34
0.45
. 2.89
to
f t
*Significant for a = 0.05 for variance components within columns.
25
The percent of the variance as it appears in the tables is a useful statistic, although
the magnitude of the values can be somewhat misleading. For this reason asterisks have
been used to indicate main effects significant at the 5% level based on F-test values (Tables
17-30).
Significant Main Effects in Determining Peak
Area Over All Soils Tested
The X-ray diffraction method used was shown to be sensitive to the variation in
mineralogy of the clay size fraction of the soils used when considering peak area. As may
be seen in Table 2, soil was shown to be the biggest source of variation. This was expected
since the soils were chosen on their apparent clay mineral composition (high smectite, low
to moderate smectite, arid no smectite).
Positioning of the slide (field/slide) was found to have a significant effect in deter­
mining peak area for.all peaks considered in this study. This points to a definite need to
be consistent in the positioning of the samples in the diffractometer. It may be further
inferred that, in attempting to use different treatments, requiring removal and reposition­
ing of the same or a different slide, a significant sourpe of variation may be incurred in
repositioning. This effect is not simply the effect of variations in the thickness of the speci­
men, but also the effect of the length of the specimen exposed to irradiation. Positioning
, of the slide significantly off center has the effect of shortening the effective length of.the
specimen irradiated by allowing a substantial portion of the incident X-ray beam to miss
the sample [39].
For Mg-saturated, ethylene glycol solvated samples, between, slide (slide/clay sepa­
ration) variations were found to have significant effects in determining peak area for the
26
7A, 3.5A and 3.3A peaks. This points to possible clay.mineral segregation during the cen­
trifuge washing technique following Mg-saturation, difference in preferred orientation,
variation of clay film thickness, or a combination of these effects. This, seems to be espe­
cially important when considering minerals in the high 26 angle region such as kaolinite
and quartz, since the peaks showing significant variation are the first order peaks for these
minerals. While these peaks also represent high order reflections for other minerals (chlo­
rite, vermiculite, and illite) similar variation was not recognized in the first order reflec­
tions for these minerals.
For these samples, variations due to the clay separation procedure were found to
be significant in determining peak area for the 14A and 7A peaks. Again this points to
clay mineral segregation, in this instance during the clay separation procedure. The effect
seems to be significant in considering chlorite and kaolinite. Vermiculite also exhibits a
first order reflection at 14A but was not recognized in many samples.
Sources of Error in Determining Clay
Mineral Composition Between Soils
The X-ray diffraction method used in this study was .found to be sensitive to the
variation in mineralogy of the clay size fraction of the soils.
As may be seen in Table 3, the soil was found to be a significant source of variation.
Soil was the major source of variation for smectite, illite, and kaolinite. This was antici.
.
I .
•
pated since the soils were chosen on their apparent clay mineral.composition.
The positioning of. the slide was also found to have a significant effect in deter­
mining the relative clay mineral composition for each of the minerals tested.
27
Table 3. Percent of Total Variance for Main Effects on the Determination of Clay Mineral
Composition Over All Soils Studied
Smectite
Illite
Kaolinite
Soil
Clay Sep./Soil
Slide/Sep.
Field/Slide
Read./Field
98.56*
0.09
0.00
1.12*
0.23
94.10*
1.44*
0.00
2.58*
1.89
87.31*
2.20*
0.00
8.19*
2.30
Coef. of Var.
6.10
. 8.33
6.80
* - significant at a = 0.05
The clay separation was found to be significant in determining the relative clay
mineral composition for all the minerals considered in this study except smectite. The
crystallite size of smectite is relatively small. Variation in temperature, time, and centri­
fuge speed not compensated for during the centrifugation procedure would have a greater
effect on the amounts of clay minerals having larger particle size than smectite.
28
II. MAIN STUDY-QUANTIFICATION
The accuracy and precision of each modification of the factor method tested in
this study were determined by linear regression analysis. In this way measured parameters,
were compared with related estimated parameters. Complete peak area measurements ap­
pear in Table 31.
Cation Exchange Capacity Estimation
. Linear regression models were developed to determine the relationship of the
cation exchange capacity of the clay-sized fraction as estimated from X-ray diffraction
results (ECEC) to the CEC of the same clay fraction as determined by chemical methods
(MCEC) for each of the modifications tested. Regression models of MCEC as estiinated
from levels of ECEC also permit an assessment of the variability of MCEC for any level
of ECEC. Table 4 contains the linear models and associated statistics developed for the ten
modifications tested in this study.
Table 4. Linear Regression Models of the Measured CEC on Estimated CEC
Mod. I
Mod. II
Mod. Ill
Mod. IV
Mod. V
Mod. VI
Mod. VII
Mod. VIII
Mod. IX
Mod. X
Slope
Intercept
0.683
0.684
.0.688
0.697
0.750
0.733
0.739
0.741
0.750
0.815
3.66
4.43
4.97
. 5.50
7.11
3.01
3.82
‘ . 4.43
5.02
6.64
* - significant at a = 0.05
r
0.927*
0.936*
0.939* ■
0.941*
0.949*
0:932*
0.935*
0.937*
0.940*
0.946*
F
SEE
0.859
0.877
0.881
0.886
0.900
0.869
0.875
0.878
0.883
0.895
6.52
6.10
6.01
5.87
5.51.
6.29
6.15
6.07
5.94
5.63
29
Based on the interdependence between MCEC and ECEC as measured by the cor­
relation coefficient (r), the coefficient of determination (r2), and the dispersion of MCEC
about the regression line as measured by the standard error of the estimate (SEE), Modi­
fications IV, V, IX, and X were chosen as the best modifications tested. Complete data
tables for these, four modifications appear in Tables 32-35.
It may be assumed that if a modification accurately accounted for the CEC as
measured by chemical methods, the regression model developed would be of the form
MCEC = ECEC, where the regression line passes through the origin and has a slope of 1.0.
The modification providing a linear relationship with a slope and y-intercept closest to
these values may be assumed to provide the most accurate assessment of the suite of clay
minerals present in the clay-sized fraction.
Statistical results for these four modifications appear in Table 5. Confidence limits
have been applied for consideration of both the inherent accuracy and precision of these
modifications.
Table 5. Selected Linear Regression Models of Measured CEC on Estimated CEC
Mod. No.
Slope
IV
V
IX
X
0.697 ±0.072
0.750+0.068
0.750+0.073
0.815+0.069
Intercept
5.50+1.66 .
7.11±1.56
5.02 ±1.68
6.64 ±1.59
r
0.94*
0.95*
. 0.94*
. 0.95*
r2
0.89
0.90
0.85
0.90
\
* - significant at a = 0.05
SEE
.
5.87
5.51
5.94
5.63
30
A value for the y-intercept greater than 0.0 is evidence of a failure of the modifi­
cation to completely account for the CEC of the clay-sized fraction as measured by chemi­
cal methods and/of the error inherent in the methods employed in obtaining values for
both MCEC and ECEC. Since the values of the y-intercepts do not significantly differ from
each other for the four models considered here it might be assumed that the error involved
in estimating CEC is constant for all of the modifications discussed. The positive intercepts
could be caused by one or more of several things. A few erroneously high measured CEC
values (MCEC) on samples dominated by low CEC clays would have this effect. Another
possible explanation is that the CEC of the clay minerals occurring in samples varied from
those assumed in estimating the CEC of the clay fraction. Alternatively, the positive inter­
cepts may indicate the presence, of additional minor, low CEC constituents of the clay­
sized fraction, such as feldspars.
Smectite, when present in a suite of clays, significantly affects both the estimated
and measured values of CEC. Overestimation of smectite would tend to reduce the slope
of these graphs to some value less than 1.0. A comparison of the slopes obtained for the
regression models of MCEC on ECEC for the four modifications discussed here reveals that
all of the modifications apparently overestimate smectite, since all of the slopes are signifi­
cantly less than 1.0 (a = 0.05). Of these four modifications, Modification X has the liighest
value for the slope of the model, coupled with favorable values for the y-intercept, .r, r2.,
and SEE.
Graphical representation of this relationship for Modification X appears in Fig. 2.
The regression model given by MCEC = 0.815 (ECEC) + 6.64 approximates the expected
relationship given by ECEC = MCEC represented by the dashed line. The graphs are simul-
31
y
r
r2
SEE
=
=
=
=
0.815x + 6.64
0.95
0.90
5.63
10 20 30 40 50 60 70 80
Estimated CEC (meq/100 g clay)
Figure 2. Linear Regression Model of Measured CEC on Estimated CEC for Modification X.
•
I
32
taneous at value of 36 meq/100 g clay. The model underestimates CEC of the clay fraction
for values of MCEC less than this value and overestimates for values greater.
Regression models of ECEC as estimated from values of MCEC provide a measure
of the ability of MCEC to predict estimated values of CEC. This approach also allows an
assessment of the variability of the estimated CEC for various levels of the measured CEC
as well as an indication of the error involved in applying the regression model at different
levels of MCEC.
If a modification is making an accurate assessment of the clay minerals in a suite of
clays, the regression model would be ECEC = MCEC. Values for the y-intercept that are
less than 0.0 would reflect either a failure of the modification to entirely account for the
actual CEC, or a use of inappropriate CEC values in estimating the. total CEC of the clay
fraction. Overestimation of the CEC could be attributed primarily to overestimation of the
smectite minerals and would result in a slope of the regression line that is significantly
greater than 1.0.
Statistical results for the four modifications discussed appear in Table 6.
Table 6. Selected Linear Regression Models of Estimated CEC on Measured CEC
Mod. No.
IV
V
IX
X
Slope
1.27±0.13
1.29±0.12
1.18±0.12
1.10±0.11
* - significant at a = 0.05
Intercept
r
r2
SEE
-2.40±2.25
-4.98+1.97
-1.46+1.73
-3.90±1.83
0.94*
0.95*
0.94*
0.95*
0.89
0.90
0.88
0.90
7.98
6.96
7.18
6.48
33
If, for any one value of CEC for the clay fraction one and only one suite of clay
minerals exists, it might be assumed that the SEE for the regression models of MCEC on
ECEC would equal the SEE for the regression models of ECEC on MCEC. Values of SEE
for the regression models of ECEC on MCEC3for all the modifications discussed, are higher
than those reported for the regression models of MCEC on ECEC, The variability of ECEC
for any level of MCEC is greater than the variability of MCEC for any value of ECEC. This
is because the clay mineral estimates exhibit greater variability than do values for measured
CEC. This indicates that, in practice, due to the variability in X-ray diffraction results, one
measured value of CEC does not represent a unique suite of clay minerals. As in the case
of the regression models of MCEC on ECEC, the mean value for the slopes and intercepts
indicate that these modifications tend to underestimate the CEC at lower levels of MCEC
and overestimate the CEC when significant amounts of smectite are present.
If any of the values for the CEC of each mineral group varies significantly from the
actual Value it would be reflected in a slope different than 1.0. The slope obtained for the
regression model testing Modification X does not significantly (a = 0.05) differ from 1.0.
The value for the y-intercept does significantly differ from 0.0. Since the y-intercepts
of the models discussed do not significantly differ from each other, the difference between
the y-intercepts of the expected model and the model actually obtained is probably due
either to erroneously high measured CEC values or to the presence of a mineral group that
was not considered in estimating the composition of the clay-sized fraction. This parallels
the results of the regression models developed for MCEC on ECEC.
From Fig. 3 it may be seen that the regression model of Modification X for ECEC
on MCEC given by ECEC = 1.10(MCEC) - 3.90, closely follows the expected relationship
34
I.IOx - 3.9
10
20
30
40
50
60
70
80
90
Measured CEC (meq/100 g clay)
Figure 3. Linear Regression Model of Estimated CEC on Measured CEC for Modification X.
35
given by ECEC = MCEC represented by the dashed line. The graphs are seen to be simul­
taneous at a value of 39 meq/100 g. The model underestimates the CEC for values of
MCEC less than this value and overestimates for values of MCEC greater than 39 meq/
100 g. The percent error may be calculated by the following:
where, y = I .IO(MCEC) - 3.90 = the predicted ECEC
and y = MCEC = the expected value of ECEC assuming ECEC = MCEC
y -y
then %-error = ------ X 100, and the sign indicates underestimation (-)
y
or overestimation (+).
From these calculations it was found that in the portion of the regression model
corresponding to values of MCEC less than 20 meq/100 g the error is greater than 11%. It
should be remembered, however, that in this portion of the graph the values of both MCEC
and ECEC are themselves small and relatively small errors in terms of meq/100 g cor­
respond to large errors when expressed as percent. At these low levels of CEC, illite and
kaolinite typically dominate the exchange complex. Consequently, small differences in the
ECEC could be the product of significant errors in estimating the amounts of these
minerals.
The percent error involved in estimating CEC from this regression model in the area
of the graph corresponding to values of MCEC greater than 30 meq/100 g is less than 5%.
Consequently, Modification X appears to be most sensitive in determining the clay mineral
composition for those clay-sized fractions containing significant amounts of smectite.
Further, Modification X provides the greatest range in values over which it acceptably esti­
mates clay mineral composition of the clay fraction.
36
Smectite Estimation
A more usable relationship is that of the estimated percent smectite composition
(ESM) as determined by the measured CEC. These regression models present a direct pre­
dictive tool for the determination of smectite based on the measured CEC of the clay­
sized fraction and permit a measure of the precision of the estimate (SEE).
Statistical results and confidence limits (a = 0.05) for the slope and y-intercept
appear in Table 7.
Table 7. Selected Linear Regression Models of Estimated Smectite Content on Measured
Cation Exchange Capacity
Mod. No.
Slope
Intercept
r
T2
SEE
IV
1.49+0.13
*1.22+0.13
-21.7812.27
0.96**
0.91
8.03
V
1.35+0.11
*1.21 ±0.11
-20.7811.94
0.96**
0.92
6.87
IX
1.37+0.12
*1.21+0.12
-20.5912.10
0.96**
0.91
7.42
X
1.23±0.10
*1.19+0.10
-19.41 + 1.78
0.96**
0.92
6.30
* - slopes of the expected regression model derived by substituting 100meq/l OOgat 100%smectite content
** - significant at a = 0.05
Expected models were derived from the regression models developed for each
modification assuming a MCEC of 100 meq/100 g at 100% smectite. This expected model
appears as a dashed line in Fig. 4 along with the graphical representation of the confidence
interval for the regression model obtained (dotted line).
;
37
.
• •//
i
10
1.23x-19.41
= 0.96
20 30 40 50 60 70 80
Measured CEC (meq/100 g clay)
90 100
Figure 4. Linear Regression Model of Estimated Smectite Content on Measured Cation
Exchange Capacity.
38
The y-intercepts obtained for these relationships did not significantly differ from
each other and are related to the x-intercepts which correspond to the average CEC of the
clay-sized fraction when no smectite is present. As may be seen from Table 7 the slopes of
the expected regression models do not significantly differ. Consequently, the expected
models are similar for all of the modifications tested.
Expected models were derived from the regression models developed for each
modification assuming a MCEC of 100 meq/100 g at 100% smectite. This expected
model appears as a dashed Ifne in Fig. 4 along with the graphical representation of the
confidence interval for the regression model obtained (dotted line).
The y-intercepts obtained for these relationships did not significantly differ from
each other and are related to the x-intercepts which correspond to the average CEC of the
clay-sized fraction when no smectite is present. As may be seen from Table 7 the slopes of
the expected regression models do not significantly differ. Consequently, the expected
models are similar for all of the modifications tested.
Overestimatioh of the percent smectite composition would tend to increase the
slopes of these relationships. Assuming that the values for the y-intercepts relate to a con­
stant and true average of the CEC of the clay-sized fraction when no smectite is present,
the preferable modification would be indicated by a regression model that closely esti­
mated the expected regression model and did not significantly differ from it. It may be
seen from Fig. 4 that this is true of the regression model developed for Modification X.
The graph of the expected and derived regression models are nearly concurrent and the
expected model lies well within the 95% confidence interval applied to the derived regres­
sion model for this modification. The coefficient of determination indicates that approxi­
39
mately 92% of the variation in the percent smectite composition was explained by vari­
ations in the measured CEC.
The error involved between the expected and the derived models was approxi­
mately 3% at MCEC = 1 0 0 meq/100 g clay. Less than 3% error is incurred in estimating
the relative smectite content at lower values of measured CEC.
A limiting factor in applying this relationship to the prediction of levels of smec­
tite content is the apparent low level of precision as indicated by an SEE = 6.30. The 95%
confidence interval for any value of the percent smectite in a sample predicted from the
measured CEC of the clay-sized fraction would be approximately ± 12.6 percent smectite.
The difference between the measured CEC (MCEC) subtracted from the estimated
CEC (ECEC) was used as a dependent variable (ECDIF) in testing relationships with ESM
to assess any effect the apparent relative smectite composition might have on estimating
accuracy. In the above discussions it was shown that accuracy is generally lower for esti­
mates of the smectite content in samples containing low amounts of smectite when the
error is expressed on a percentage basis. The regression models developed for ECDIF on
ESM provide a direct indication of bias and an avenue for determining the significance of
the apparent bias.
Statistical results for the four best modifications tested appear in Table 8. Confi­
dence limits have been applied to the slope and y-intercept to facilitate the assessment of
the significance of the apparent bias implied by the slope and intercept of the model.
Modifications providing accurate and unbiased estimates of the suite of clay min­
erals should reveal a relationship that is concurrent with the x-axis and is of the form
ECDIF = 0, with r = 0, r2 = 0, and SEE = 0.0. Regression models testing the modifications
40
Table 8. Selected Linear Regression Models of the Difference in Estimated and Measured
Cation Exchange Capacity on Estimated Smectite Content
Mod. No.
Slope
IV
V
IX
X
0.248+0.067
0.217 ±0.067
0.198 ±0.073
0.151 ±0.076
Intercept ..
-0.32±1.77
-3.81 ±1.62
-0.63 ±1.79
-3.83 ±1.66
r
0.73*
0.68*
0.62*
0.50*
r2
SEE
0.53
0.46
0.38
0.25
6.28
5.72
6.33
5.86
* - significant a t« = 0.05
that significantly differ from this perfect fit relationship indicate significant bias in making
estimates of the clay mineral composition. Ovefestimation of the amount of smectite
would tend to increase the slopes of these models and decrease the value o f the y-intercept.
Of primary importance in analyzing these relationships is the slope and y-intercept
of the regression models obtained. From Table 8 it may be seen that the slopes of all the
regression models significantly differ from 0.0. Consequently, it may be assumed that bias
is incurred in estimating the clay mineral composition by any of the four modifications dis­
cussed. However, the results indicate that Modification X provides the most accurate and
relatively unbiased assessment of the clay mineral composition. Modification X has the
lowest slope; Modifications IV and IX do include 0.0 in the 95% confidence interval. The
y-intercept for Modification X is reasonably close to zero. In addition the r, r2, and SEE
values for Modification X are lowest of the modifications discussed.
These results tend to support those previously reported for the regression models
developed for ECEC on MCEC, MCEC on ECEC and ESM on MCEC. From Fig. 5 it is
observed that the graphs of the expected and derived models are simultaneous at a value
41
y = 0.151x-3.83
r = 0.499
I2 = 0.249
SEE = 5.86
10 20 30 40 50 60 70 80
Estimated Smectite Content (%)
Figure 5. Linear Regression Model of the Difference in Estimated and Measured Cation
Exchange Capacity on Estimated Smectite Content.
42
of approximately 25 percent smectite. The regression model indicates that Modification
X tends to overestimate the amount of smectite present when it is greater than this amount
and underestimate the amount o f smectite when it is less than this amount. Modification X
also tends to favor lower estimated amounts of illite. In the portion of the graph represent­
ing low smectite composition the suite of clay minerals would be dominated by illite and
kaolinite. Consequently, Modification X should be expected to yield lower estimates of the
CEC in samples dominated by illite.
Illite Estimation
As a further test of the accuracy of the mineral estimates, regression models were
developed to examine the relationship of the relative composition of illite (EIL) in each
sample with the percent illite based on total K analysis assuming 8.3% (MILS) and 5.1%
(MILS) elemental K per unit cell of illite. Regression models o f EIL as estimated from
values of MILS and MILS provide a measure of the sensitivity of the chemical methods
employed to account for variation in apparent percent composition of illite in the clay­
sized fraction. They also allow an assessment of the variability of the estimated percent
illite for various levels of MILS and MILS as well as the error involved in applying the
regression model at various levels on MILS and MILS.
It may be assumed that if a modification accurately estimated the percent illite
and all of the K. present in the clay-sized fraction was a component of the crystalline
structure of illite then the expected regression model developed would be PIL = MILS
or MILS. This regression line would pass through the origin and have a slope of 1.0. The
modification providing a linear relationship with a slope and y-intercept closest to these
43
values may be assumed to provide the most accurate assessment of the relative amount of
illite present in the clay-sized fraction. Values for the y-intercept that are less than 0.0
would reflect a failure of the modification to entirely account for the relative amount of
illite as estimated by total K analysis.
Models derived assuming 8.3% elemental K per unit cell illite. Statistical results for
the four best modifications appear in Table 9. Confidence limits (a = 0.05) have been ap­
plied for consideration of both the accuracy and the precision of these modifications.
Table 9. Selected Linear Regression Models of Estimated Illite Content on Measured Illite
Content (Assuming 8.3% K per Unit Cell Illite)
Mod. No.
IV
V
IX
X
Slope
1.63 ±0.24
1.03 ±0.15
1.58±0.23
0.99 ±0.15
Intercept
-11.12±1.73
-4.83±1.10
-9.22±1.67 .
-3.31±1.09
r
0.87*
0.87*
0.87*
0.86*
r$
SEE
0.75
0.75
0.76
0.74
6.10
3.90
5.92
3.87
* - significant at a = 0.05
The y-intercepts of all the regression models (Table 9) are significantly less than
0.0. These negative intercepts support the conclusions made from the regression models
developed for ECEC on MCEC, particularly that the inability of the modifications to com­
pletely explain the percent illite derived from total K analysis is due to the presence of a
K-bearing mineral in the clay-sized fraction that caused an overestimation of the relative
amount of illite. It may be seen, however, that there is a significant difference between the
y-intercepts obtained for these models. While the y-intercepts of the regression models for
Modifications IV and IX do pot significantly differ from each other, they do significantly
44
differ from the intercepts obtained for the models testing Modifications V and X. The
latter modifications do not significantly differ from each other. It should be noted that
Modifications IV and IX tend to cause higher estimates of smectite and illite while Modi­
fications V and X tend to favor higher estimates of kaolinite at the expense of the esti­
mated smectite and illite contents.
If the modification is sensitive to the changes in illite content as determined by
total potassium analysis and the K-content of the illite is 8.3%, the slope of the regres­
sion model testing that modification should not significantly differ from 1.0. In Figs. 6
and 7 it may be seen that the regression models closely parallel the expected models and
differ in both cases by a relatively constant amount.
The constancy of the difference between the expected and derived regression
model might also indicate the use of an inappropriate combination of coefficients in
the characterization of the peak areas. As stated earlier it might be reasonable to expect
such a relationship if the procedure used to estimate the mineral components of the clay­
sized fraction failed to recognize a K-bearing mineral o f minor, relatively constant,
proportions.
Values for SEE indicate lower variability for EIL at any given level of MILS for
Modifications V and X. SEE values were much higher for the regression models testing
Modifications IV and IX.
Modification X seems to provide the most favorable combination o f accuracy and
precision for the estimation of illite of the four modifications discussed here. The regres­
sion model testing this modification is given by EIL = 0.99 (MILS) - 3.31. This closely folr
lows the expected relationship given by EIL = MILSi The coefficient of determination
45
10
20
30
40
Measured Fllite Content (%)
50
60
Figure 6. Linear Regession Model of Estimated Illite Content on Measured Illite Content
(8.3% K) for Modification V.
46
0.99x-3.31
Measured Dlite Content (%)
Figure 7. Linear Regression Model of Estimated Illite Content on Measured Illite Content
(8.3% K) for Modification X.
47
indicates that 75% of the variation in the EIL values was explained by the variation of
the MILS values. This is considered further evidence of the presence of additional K-bearing minerals in the clay-sized fraction.
The percent error was dependent on the relative amount of illite present, with
more error, on a percent basis, being incurred on the estimation of low amounts o f illite.
The percent error was greatly reduced, to about 10%, in considering estimates of larger
amounts of illite. This parallels the findings reported by several authors and might be antic­
ipated from the parallel nature o f the expected and derived models.
Models derived assuming 5.1% elemental K per unit cell illite. The effect of assum­
ing 5.1% K per unit cell of illite is to increase the measured relative composition of illite in
all samples compared to values derived assuming 8.3% elemental K. Modifications IV and
IX favor higher estimates o f smectite and illite. Based on the regression models developed
for EIL on MILS, it was anticipated that the estimated illite composition derived by these
two modifications might more closely relate to the measured illite composition assuming
5.1% K per unit cell illite rather than 8.3% K.
Table 10 contains the statistical results for the four best modifications tested.
Table 10. Selected Linear Regression Models of Estimated Illite Content on Measured
Illite Content (Assuming 5.1% K per Unit Cell Illite)
Mod. No.
Slope
Intercept
IV
V
IX
X
1.00±0.04
0.63 ±0.03
0.97 ±0.04
0.61 ±0.03
-11.12±0.50
-4.83±0.40
-9.22±0.47
-3.31±0.38
*
- significant at a = 0.05
r
0.87«"
0.87*
0.87*
0.86*
.
I2
SEE
0.75
0.75
0.76
0.74
1.75
1.40
1.67
1.35
48
The slopes of the regression models testing Modifications IV and IX do not differ
from the perfect fit slope of 1.0. However, these modifications more seriously underesti­
mated relative E ite content in comparison with measured values assuming 5.1% K per unit
cell illite than did Modifications V and X in similar comparisons assuming 8.3% K. These
results indicate that for the samples used in this study the 8.3% value is a more accurate
measure for the relative K-content per unit cell E ite than is 5.1%. Consequently, the dis­
cussion and conclusions drawn based on the models of EIL derived from MILS appear to
be more appropriate.
To assess the bias in estimating the relative E ite composition that is related to the
estimated percent composition of Eite, the difference between MILS subtracted from EIL
was used as a dependent variable (ILDIF8) in developing regression models with EIL. Sta­
tistical results for the four best modifications tested appear in Table 11.
Table 11. Selected Linear Regression Models of the Difference in Estimated and Measured
Illite Contents on Estimated Illite Content (Assuming 5;1% K per Unit Cell IEte)
Mod. No.
Slope
IV
V
IX
X
0.519 ±0.075
0.237 ±0.116
0.501 ±0.077
0.219±0.124
Intercept
-10.30±0.98
-8.61 ±0.97
-9.46 ±0.98
-7.83 ±1.00
i
0.89*
0.51*
0.88*
0.45*
r2
SEE
0.80
0.26
0.78
0.45
3.48
3.43
3.45
3.54
* - significant at a = 0.05
Modifications providing accurate and unbiased estimates of the suite of clay min­
erals should reveal a relationsEp that is concurrent with the x-axis and is of the form
ILDIF8 = 0, with r = 0, r2 = 0 , and SEE = 0. Underestimation of the relative amount of
49
illite present would tend to decrease the value of the y-intercept. A positive slope for the
regression line indicates that the modification provides biased estimates of the percent
illite composition such that, above some point at which the derived and expected models
are simultaneous, the amount of overestimation is directly proportional to an increase in
the apparent relative composition of illite. Conversely, the amount of underestimation is
directly prdportipnal to a decrease in the percent illite composition. In addition, statisti­
cally significant values for the r and r2 further indicate that the bias inherent in the modi­
fication is significant.
From Table 11 it may be seen that the slope and correlation coefficients of all
the regression models discussed significantly differ from 0.0. It follows that bias is incur­
red in estimating the relative composition of illite by any of the modifications discussed
here. It may be anticipated, from the results o f the regression models developed for EIL
on MILS (Table 9) that the y-intercepts will significantly differ from 0.0. This was found
to be the case for all four modifications discussed.
Modifications X and V combine the lowest slope with a value for the y-intercept
that is in line with the results obtained for EIL on MILS. The r and r2 values are the lowest
of the modifications discussed. The SEE is slightly higher for Modification X, but it is not
felt that this indicates a significant increase in variabUity of the estimates compared to the
other modifications.
The regression model as shown in Fig. 8 indicates that Modification X underesti­
mates the relative amount of illite present below a value of 35.8% illite (EIL). This cor­
responds to the upper range of the percent illite composition as estimated by Modification
X. Consistent apparent underestimation of EIL coupled with a low, yet significant cor-
50
0.219x - 7.83
r = 0.454
T 2 = 0.206
SEE = 3.54
Estimated Illite Content (%)
Figure 8. Linear Regression Model of the Difference in Estimated and Measured Illite Con­
tent on Estimated Illite Content (assuming 8.3% K per unit cell IHite).
51
relation coefficient, is interpreted to indicate a consistent overestimation of MILS. This
could be due to the presence of. an additional, but unmeasured, K-bearing mineral that
composes a small, relatively constant portion of the clay-sized fraction. However, a defi­
nite conclusion based on the results of this study concerning the apparent underestimation
of illite is not possible. When the results of these regression models are considered in con­
junction with the results previously reported here, it is felt that they indicate Modification
X is more responsive to the amount of illite in a sample.
Kaolinite Estimation
Measurements of the kaolinite content such as those made for illite content were
not made during this study. As a result the accuracy and precision o f a modification’s
ability to estimate the relative composition of kaolinite was inferred from linear regression
models of the estimated kaolinite content (EKA) on the measured CEC (MCEC). Statistical
results and confidence limits (oz = 0.05) for the slope and intercept appear in Table 12 for
the four best modifications tested.
Table 12. Selected Linear Regression Models of Estimated Kaolinite Content on Measured
Cation Exchange Capacity
Mod. No.
Slope
Intercept
r
IV
V
IX
X
-1.05 ±0.17
-1.22±0.16
-1.02±0.16
-1.17±0.16
68.45 ±2.87
87.39±2.77
. 68.36 ±2.74
86.96±2,68
-0.88*
-0.91*
-0.88*
-0.91*
* - significant at a = 0.05
r?
q.77 .
0.83
0.77
0.82
SEE
9.98
9.79
9.70
9.49
52
In general, samples exhibiting low values for measured CEC will possess high kaolinite contents and low smectite content. The reverse is assumed to be true at high values for
measured CEC. As a result the slopes of the regression models o f EKA oh MCEC should be
negative. As may be seen in Table 12 the slopes of the regression models testing the four
modifications discussed exhibit this negative relationship.
Kaolinite typically exhibits a relatively small CEC. In the presence of measureable
amounts of smectite, kaolinite is expected to compose a relatively small portion of the
total CEC of the clay-sized fraction. Further, it is assumed that relatively large Variations in
the estimated kaolinite content would not affect the CEC of the clay fraction as much as
a similar variation in smectite content. Consequently, it could be anticipated that the
I
accuracy and precision of the modifications as measured by the regression models o f EKA
on MCEC would be lower than that indicated by similar models developed for smectite
composition. The high values for the SEE obtained for all the modifications tested indicate
that these modifications estimate kaolinite content with less precision than either smectite
or illite. Modification X exhibited the lowest SEE (9.49).
The four modifications discussed exhibit significant correlation between the esti­
mated kaolinite content and the measured CEC. The values of the intercepts and their
confidence intervals indicate that all four modifications significantly underestimate kaoli­
nite at 100% kaolinite content. Modifications V and X tend to favor higher estimates for
kaolinite. These two modifications significantly differed from Modifications IV and IX but
not from each other. Since regression models testing the estimation of smectite and illite
content indicated that Modification X provided the best estimates of these minerals it
was assumed that this modification provided adequate estimation o f kaolinite content as
53
well. The regression model for Modification X is given by EKA = -1.17 (MCEC) + 86.96,
with r = -0.91, r2 = 0.82, and SEE = 9.49. This relation is graphically presented in Fig. 9.
Linear regression models of ECDIF as related to EKA were developed to assess the
effect of the relative kaolinite composition has on the estimating accuracy. They appear in
Table 13.
Table 13. Selected Linear Regression Models of the Difference in Estimated and Measured
Cation Exchange Capacity on Estimated Kaolinite Content
Mod. No.
Slope
Intercept
r
r2
SEE
IV
V
IX
X
-0.318±0.1p6
-0.223 ±0.096
-0.238±0.106 .
-0.150±0.096
17.28±1.81
12.09±1.63
. 12.55±1.82
6.64±1.66
-0.72*
-0.67*
-0.60*
-0.50*
0.52
0.50
0.36
0.25
8.69
7.20
7.31
6.03
* - significant at a = 0.05
The expected regression model is concurrent with the x-axis and is of the form
ECDIF = 0, with r = 0, r2 = 0, and SEE = 0. A significant difference between this perfect
fit model and the derived model indiates a significant bias in making estimates of the kaoli­
nite content. Underestimation of the kaolinite content would tend to steepen the slopes of
the regression models and mcrease the value of the y-intercept. Data in Table 13 show that
. the slopes and y-intercepts significantly differ from 0.0. The correlation coefficients indi­
cate relationships significant at a = 0.05. It may be assumed that bias is incurred in estimat­
ing the relatively kaolinite content. The results indicate that Modification X provides the
most accurate and relatively unbiased assessment of the kaolinite composition. It combines
54
-1.17x + 86.96
-0.91
SEE = 9.49
10
20 30 40 50 60 70 80
Measured CEC (meq/100 g clay)
90
100
Figure 9. Linear Regression Model of Estimated Kaolinite Content on Measured Cation
Exchange Capacity.
55
the lowest slope and y-intercept with the lowest value of r, r2, and SEE for any of the
modifications discussed.
These results seem to corroborate those previously reported for estimates of smec­
tite and illite composition. The graphs of the expected and derived models for Modifi­
cation X (Fig. 10) are simultaneous at a value of approximately 44% kaplinite. This indi­
cates that Modification X underestimates CEC o f the clay fraction at kaolinite contents
higher than 44% and overestimates CEC at kaolinite contents lower than this value. This
could result from an underestimation of kaolinite and/or an overestimation of smectite.
Previously it was shown that Modification X overestimates CEC and smectite at values of
smectite composition greater than 25 percent. The results indicate that Modification X
tends to underestimate kaolinite and overestimate smectite at values of relative kaolinite
and smectite composition greater than 44% and 25%, respectively. An apparent overesti­
mation of kaolinite and underestimation of smectite occurs at compositions below these
values. Since regression models testing the accuracy of the illite estimations indicated a
consistent error not directly involved with the X-ray diffraction pattern characterization
• .-
process, it is inferred that Modification X overestimates smectite and underestimates
kaolinite. These results indicate that further accuracy might be obtained by trying other
modifications of the factor method that reduce the characterized peak area o f the 17A
peak while it increases the characterized peak area o f the 7A peak.
56
y = -0.150x + 6.64
r = -0.50
T2 = 0.25
SEE = 6.03
— e.
10
20 30 40 50 60 70 80
Estimated Kaolinite Content (%)
90
Figure 10. Linear Regression Model of the Difference in Estimated and Measured Cation
Exchange Capacity on Estimated Kaolinite Content.
SUMMARY AND CONCLUSIONS
An assessment of the major sources of error in the X-ray diffraction procedure
was conducted in a preliminary study using a one-way analysis of variance for a nested
design for peak area and percent mineral composition. When considered over all soils
tested, the X-ray diffraction method used was found to be sensitive to the variations in
the mineralogy of the clay fraction of the soils used when considering peak area and rela­
tive mineral composition. The positioning of the slide was found to be significant in
determining peak area and relative composition for all soils tested. Clay separation and
between slide effects were found to be significant sources of variation in specific instances
and seem to be particularly important in considering kaolinite content and those peaks
associated with kaolinite determination. The results indicate the need for extreme care and
consistency during all phases of sample preparation and presentation.
In the main study the accuracy of ten modifications of the factor method was
investigated. The results indicate that the factor method may be applied in X-ray diffrac­
tion analysis to yield a relatively fast and reasonably accurate assessment of the dominant
clay minerals composing the clay fraction of arid and semi-arid land soils and their parent
material in southeastern Montana. The method seems particularly useful in making quantitative estimations of smectite, illite, and kaolinite.
Linear regression models indicated that Modification X is most responsive to the
amount of smectite, illite and kaolinite in a sample. This modification yields accurate esti­
mates for these clay minerals in material that does not contain significant amount of vermiculite and chlorite.
The following computations are used to calculate characterized peak areas for
Modification X:
58
17A Mg-sat. E.G./5
= Smectite Peak Area
(14A Mg-sat. E.G. minus 14A K-sat. 350°C/2
= Vermiculite Peak Area
14A K-sat. 350°C/2
= Chlorite Peak Area
IOA Mg-sat. E.G ./1
. = Illite Peak Area
(7A Mg-sat. E.G. minus 7A K-sat. 550°C)/4
= Kaolinite Peak Area
(3.3A Mg-sat. E.G. minus 3/4 ( IOA Mg-sat. E.G.))/4
= Quartz Peak Area
Characterized peak areas are totaled and the relative percent composition of each mineral
calculated according to:
Smec. Pk. Area + Verm. Pk. Area + Chlor. Pk. Area
+ KaoL Pk. Area + Quar. Pk. Area = Total Peak Area
Percent Smectite = Smec. Pk. Area/Total Pk. Area X 100
Percent Vermiculite = Verm. Pk. Area/Total Pk. Area X 100
Percent Chlorite = Chlor. Pk. Area/Total Pk. Area X 100
Percent Illite = 111. Pk. Area/Total Pk. Area X 100
Percent Kaolinite = Kaol. Pk. Area/Total Pk. Area X 100
Percent Quartz = Quar. Pk. Area/Total Pk. Area X 100
Linear regression models involving CEC determined by chemical means (MCEC)
.
and the CEC estimated from X-ray diffraction analysis (ECEC) showed that 90% of the
variability of the predicted parameter could be accounted for by the measured parameter
using estimates derived by Modification X. The variability of ECEC for any level of MCEC
is greater than the variability of MCEC for any level of ECEC. This indicates that in prac,
tice, due to the variability in the X-ray results, one measured value of CEC does not repre­
sent a unique suite of clay minerals as determined by X-ray diffraction analysis.
Measurement of illite content by total K analysis was conducted assuming 8.3%
and 5.1% elemental K per unit cell illite. The results of linear regression analysis indicated
59
that measurements made using the 8.3% K value more accurately depicted the estimated
illite content.
Using estimates derived by Modification X predictive regression models for the esti­
mation of the relative compositions of smectite, illite and kaolinite were developed based
on values of measured CEC and the percent composition of illite as determined by total K
analysis (MILS):
%-smectite (± 12.6%)= 1.23(MCEC) - 19.41, r2> 0.92
%-illite . (+; 7.7%)= 0.99(M ILS)- 3.31,
r2 =0.74
%-kaolinite(± 19.0%) = -1 .1 7 (MCEC) + 86.96,r2 = 0.82 .
The relative amount of illite was frequently underestimated. The apparent under­
estimation could be caused by variability in the K per unit cell of illite resulting in over­
estimation of illite from total K analysis. This is supported by the moderate r2 value. Im­
proper factors employed in characterizing peak areas might have been responsible for the
apparent underestimation, but, this is not supported by the slope of the regression. Alter­
natively, the y-intercept of this model could indicate either a threshold amount of illite
that must be present to be recognized by the X-ray diffraction machine or could indicate
the presence of an additional, K-bearing, nonmicaceous mineral such as feldspar in small
constant amounts that was not considered in estimating the mineral composition of the
clay-sized fraction of the samples studied.
Modification X fended to overestimate smectite and underestimate kaolinite at
values of relative smectite and kaolinite composition greater than 25% and 44%, respec­
tively. An apparent overestimation of kaolinite and underestimation of smectite occurs
at compositions below these values. Since regression models testing the accuracy of the
60
illite estimations indicated a consistent error not directly involved with the X-ray diffrac­
tion pattern characterization process, it was inferred that Modification X overestimates
smectite and underestimates kaolinite.
Significant bias caused by the apparent amount of the mineral present was found
for all modifications tested in estimating smectite, illite and kaolinite. However, Modifi­
cation X was shown to be least affected by the amount of mineral present. Based on a
comparison of the SEE and r2 values, the estimates of the relative illite composition ap­
pear to be less accurate than estimates of the relative smectite content. Illite and smectite
are estimated with greater accuracy and precision than kaolinite.
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64
26. Kunze, G. W. 1955. Anomalies in the ethylene glycol solvation techniques used in
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...
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59. Wilding, L. D. Procedure as written in mimeographed laboratory handout.
APPENDIX
Table 14. ANOVA Table (Over AU Three SoUs Tested)
MS
F
Expected MS
ssSoils
2
MSSoils
bcdn
^2+nffDCC + ndffCCB
+ ndcffBCA
x ^ u Sff2
+ ndcbP T
abcdn
abcdn
6 SS(SZSY)2 _ S(SSSSY)2
ab cdn
bcdn
^sClay Sep.
6
^ sClay Sep.
MSglide
ff2 +nofjec + ndofceg
+ ndcffBCA
Yc - Yg Among Slides
within Clay Sep.
ab c dn
ab cdn
18 SSS(SSY)2 _ SS(SSSY)2
dn
cdn
ssSlide
18
msSMc
ff2+nffDCC+ ndffCCB
Yq - Y q Among Field/Slide
within Slides
abcdn
abcdn
54 SSSS(SY)2 _ SSS(SSY)2 ssFieldZSlide
n
dn
54
Source of Variation
-Y
Among Soils
Y g -Y ^ Among Clay Sep.
within Soils
Y - Y d Within Field/Slide
(Read/Field)
TOTAL
Soils = 3
Clay Sep. = 3
Slide = 3
Field/Slide = 3
Read/Slide = 3
DF
2
162
242
SS
abcdn
S(SSSSY)2 -CT
abcdn
abed n
SSSSSY2 - SSSS(SY)2
n
abcdn
SSSSSY2 - CT
ab cdn
C.T. = (SSSSSY)2
abcdn
ssReadZField
162
MSClay Sep.
MsFieldZSMe
MsFieldZSMe
MSRead/Field
ff2+nffDCC
a2
Table 15. Peak Area Measurements (m2) for the Preliminary Study
Sample
No.
11111
11112
11113
11121
11122
11123
11131
11132
11133
11211
11212
11213
11221
11222
11223
11231
11232
11233
11311
11312
11313
11321
11322
11323
11331
11332
11333
12111
12112
12113
12121
12122
12123
12131
12132
12211
12212
12213
12221
12222
12223
17A
Mg-EG
5.10
7.92
5.00
3.19
3.24
3.70
4.23
4.21
4.13
4.70
4.70
4.70
4.05
4.55
4.63
5.39
' 6.12
5.69
5.00
4.50
5.05
3.84
4.37
4.37
6.53
7.25
6.47
4.60
4.14
4.23
3.78
4.10
3.36
2.42
2.42
4.50
4.79
5.30
4.85
3.84
4.23
IOA
Mg-EG
14A
Mg-EG
14A
K350
7A
K350
0.21
0.24
0.18
0.14
0.28
0.23
0.16
0.17
0.14
0.22
0.23
0.16
0.27
0.18
0.23
0.24
0.18
0.18 .
0.24
0.22
0.20
0.20
0.22
0.22
0.25
0.28
0.26
0.17
0.18
0.16
0.14
0.14
0.16
0.19
0.15
0.18
0.25
0.21
0.18
0.17
0.18
0.19
0.36
0.36
0.15
0.25
0.27
0.29
0.15
0.28
0.27
0.23
0.25
0.26
0.25
0.19
0.19
0.28
0.28
0.28
0.24
0.28
0.21
0.15
0.25
0.35
0.40
0.40
0.18
0.21
0.18
0.18
0.20
0.24
0.21
0.20
0.31
0.28
0.31
0.14
0.21
0.21
0.50
0.56
0.43
0.23
0.22
0.31
0.36
0.40
0.32
0.36
0.45
0.39
0.24
0.23
0.17
0.62
0.74
0.77
0.47
0:47
0.43
0.21
0.30
0.27
0.78
0.67
0.76
0.47
0.58
0.37
0.27
0.23
0.41
0.60
0.51
0.29
0.45
0.28
0.21
0.21
0.13
1.35
1.30
1.31
1.16
1.16
1.19
1.41
1.45
1.49
1.23
1.24
1.24
0.90
0.88
0.91
1.33
1.31
1.29
1.30
1.35
1.35
0.79
0.79
0.79
1.27
1.26
1.25
1.33
1.38
1.31
1.28
1.31
1.31
1.30
1.30
2.07
2.08
2.07
1.19
1.26
1.25
7A
MgEG
0.94
0.95
0.93
1.08
1.08
0.93
0.75
0.75
0.75
1.05
1.05
1.05
0.95
0.95
0.90
0.89
0.87
1.07
1.19
1.20
1.21
1.11
1.13
1.16
1.25
. 1.27
1.27
1.03
1.04
1.05
0.97
0.96
1.00
0.75
0.77
1.17
1.16
1.20
1.09
1.09
1.15
3.5A
MgEG
0.46
0.46
0.46
0.42
0.44
0.44
0.40
0.42
0.40
0.58
0.57
0.60
0.46
0.46
0.46
0.40
0.40
0.50
0.66
0.66
0.68
0.62
0.60
Q.60
0.60
0.58
0.60
0.52
0.50
0.48
.0.54
0.50
0.52
0.33
0.32
0.61
0.62
0.58
0.61
0.64
0.60
3.3A
MgEG
0.50
0.42
0.44
0.66
0.66
0.65
0.55
0.49
0.61
0.53
0.44
0.44
0.61
0.66
0.72
0.60
0.59
0.59
0.63
0.56
0.60
0.65
0.63
0.70
0.60
0.63
0.70
0.50
0.50
0.55
0.60
. 0.55
0.55
0.38
0.34
0.55
0.55
0.55
. 0.60
0.63
0.65
70
Table 15 (continued)
Sample
No.
17A
Mg-EG
IOA
Mg-EG
14A
Mg-EG
12231
12232
12233
12311
12312
12313
12321
12322
12323
12331
12332
12333
13111
13112
13113
13121
13122
13123
13131
13132
13133
13211
13212
13213
13221
13222
13223
13231
13232
13233 .
13311
13312
13313
13321
13322
13323
13331
13332
13333
21111
21112
6.13
6.13
6.25
4.55
4.27
4.19
3.85
3.47
3.28
6.46
6.00
6.25
4.73
4.67
4.73
3.11
2.65
2.29
4.23
4.50
4.74
4.41
4.55
4.50
3.35
2.88
2.88
5.40
5.52
5.58
4.30
4.16
4.50
4.05
3.96
3.87
7.25
7.97
7.84
0.00
0.00
0.20
0.23
0.20
0.20
0.19
0.17
0.18
0.15
0.12
0.13
0.15
0.18
0.16
0.14
0.20
0.09
0.10
0.08
0.14
0.12
0.11
0.14
0.11
0.13
0.10
0.09
0.09
0.09
0.09
0.13
0.12
0.12
0.17
0.12
0.13
0.14
0.21
0.16
0.14
0.40
0.37
0.32
0.51
0.28
0.39
0.32
0.57
0.30
0.35
0.21
0.49
0.24
0.36
0.13
0.27
0.16
0.12
0.14
0.23
0.25
0.54
0.28
0.56
0.45
0.32
'0.34
0.21
0.23
0.39
0.45
0.22
0.16
0.13
0.09
0.19
0.11
0.19
0.23
0.67
0.13
0.47
0.10
0.45
0.28
0.52
0.45
0.21
0.26
0.39
0.25
0.12
0.15
0.06
0.20
0.20
0.06
0.64
0.15
0.49
0.08
0.64
0.62
0.17
0.45
0.16
. 0.65
0.21
0.25
0.18
0.20
0.19
0.17
0.19
0.68
0.26
0.28
0.60
0.25
0.54
0.15 .
0.51
0.45
0.21
.
14A
K350
7A
K350
1.87
1.86
1.86
1.29
1.25
1.22
0.95
0.97
1.01
1.38
1.38
1.37
1.41
1.45
1.44
1.24
1.25
1.23
1.63
1.59
1.61
1.26
1.23
. 1.26
0.86
0.86
0.89
1.46
1.46
1.39
1.57
1.65
1.57
1.53
1.50
1.45
1.69
1.70
1.73
0.71
0.67
7A
MgEG
0.97
0.94
0.97
0.96
0.97
0.99
0.86
0.93
0.83
. 0.87
0.89
0.94
0.81
0.77
0.77
0.83
0.74
0.70
0.43
0.49
0.44
1.03
1.01
1.01
0.73
0.73
0.74
0.60
0.65
0.61
0.99
0.90
0.96
1.09
1.12
1.10
1.10
1.14
1.09
1.11
1.13
3.5A
MgEG
3.3A
MgEG
0.38
0.40
0.38
0.52
0.52
0.48
0.40
0.44
0.42
0.48
0.46
0.44
0.28
0.33
0.45
0.40
0.44
0.42
0.20
0.25
0.37
0.52
0.48
0.48
0.36
0.36
0.38
0.29
0.31
0.31
0.50
.0.53
0.54
0.64
0.64
0.66
0.56
0.55
0.53
0.47
0.49
0.50
0.49
0.52
0.55
0.48
0.55
0.50
0.50
0.50
0.50
0.55
0.55
0.27
0.27
0.39
0.48
0.36
0.40
0.20
0.24
0.16
0.57
0.50
0.54
0.34
0.32
0.34
0.30
0.28
0.28
0.50
6.54
0.56
0.48
0.52
0.56
0.44
0.50
0.48
0.47
0.54
71
Table 15 (continued)
I OA
Mg-EG .
14A
Mg-EG
Sample
No. '
17A
Mg-EG
21113
21121
211.22
21123
21131
21132
21133
21211
21212.
21213
21221
21222
21223
21231 ■
21232
21233
21311
21312
21313
21321
21322
21323
21331
21332
21333
22111
22112
22113.
22121
22122
22123
22131
22132
22133
22211
22212
22213
22221
22222
22223 •
22231
0.15
0.33
0.00
0.27
0.06
0.00
0.28
0.10
0.00
0.08
. 0.28
0.00
0.15
0.36
0.00
0.35
0.16
0.00
0.17
0.45
ti.00
0.35
0.20
0.00
0:24
0,00
0.39
0.28
0:41
0.00
0.51
0.17
0.00.
0.19
0.00 .
0.49
0.48
0,15
0.00
0.26
0.38
0.00
0.16
0.00 .
0.49
0.24
0.39
0.00
0.14
0.40
0.00
0.48
0.19
0.00
0.17
0.52
0.00
0.14
0.43
0.00
0.20
0.44
0.00
0.13
0.43
0.00
0.29
0.89
0:00 .
0.25
0.87
0.00
0.32
0.71
0.00
0.73
0.21
0.00
• 0.44
0.21
0.00
0.44
0.21
0.00
0116
0.49 '
0.00
0.14
0.51
0.00
0.17
0.51
0.00
0.47
0.41
0.00
• 0.37
0.47
0.00
0.30
0.49
0.00
0.16
0.47
0.00
0.40
0.21
0.00
0.18
0.47
0.00
0.17
0.55
0.00
0.18
0.00 . 0.53
0.20
0.52
0.00
0.30
0.68
0.00
14A
K350
.
.
.
■
Ik
■ K35'0
,A .
MgEG
0.69
0.41
1.16
0.36 • 1.21
0.22
0.44
0.22 .
1.19
0.44
1.15
0.22
0.64
0.50
1.19
0.60
0.57
1.17
1.15
0.62
. 0.59
0.50
0.42
1.27
0.44
0.41
1.31
0.53
1.31
. 0.44
0.25
0.25
1.74
0.25
■
1.73
0.27
0.25
1.71
0.23
0.86
1.35
0.42
0.47
0.89
1.32 ■
0.92
1.33
0.41
2.04
0.69
0.52
2.05
0.44
0.69
0.80
’■ 0.44 .
2.07
1.75
0.25
. .0.35 .
0.32
1.73
0.31
■ 0.33
1.73
0.25
0.92
0.65
2.16
1.07
2.23
0.57
2.22
0.47
0.91
1.03
1.41
0.36 .
0.97
1.39
0.39
1.03
1.49
0.29
0.60
. 1.99
0.20
0.25
0.62
2.04
0.64
2.09 •
0.20
1,02
1.53
0.43
.0.90
1.51
0.47
L43
0.44
1.01
0.81
1.36
0.47
0.85
1.56
0.39
0.84
1.39
0.51
0.57
2.09
0.25
0.53.
. 2.01
. 0.25
0.48
2.05
0.28
1.09
2.04
0.50
3.5A
MgEG
0.59
0.65
0.72
0:77
0.53
0.60
0.51
0.73
0.69
.0.63
0.99
0.99
0.85
0.92
0.71
0.94
1.13
0.99
1.03
0.90
0.93
1.07
1.29
1.25
1.05
0.64
0.51
0.60
0.86
0.71
0.73
0.65
0.53
0.51
0.67
0.66
0.65
1.03
0.99
0.96
0.77
3.3A
MgEG
0.47
0.70
0.68
0.61
0.58
0.58
0.58
0.70
0.61
0.67
. 0.89
. 0.87 .
1.00
0.68
0.68 .
0.58
0.96
1,08
1.06
0.84
0.92
0.94
1.04
1,08
1.08
0.59 .
0.68 .
. 0.72
0.79
0.96
. 0.94
0.59
0.68
0.72
. 0.68
0.76
0.76
1.10
1.10
1.06
0.88
72
Table 15 (continued)
Sample
No.
17A
Mg-EG
0.00
22232
0.00
22233:
22311
0.00
0.00
22312
0.00
22313
0.00
22321
0.00
22322
0.00
22323
22331
0.00
0.00
.
22332
0.00
22333
23111 ■ 0.00
0.00
23112
0.00 .
23113.
0.00 .
23121
0.00
23122
0.00
23123
0.00
23131
0.00
23132
0.00
23133
0.00
23211
0.00
23212
0.00
23213
0.00
23221
0.00
23222
0.00
23223
0.00
23231
0.00
23232
0.00
23233
0.00
23311
0.00
23312
0.00
23313
. 0.00
23321.
0.00
23322
.0.00 .
23323
0.00
23331
0.00
23332
0.00
23333
0.86
31111
0.91
31112
1.03
31113
t
14A
IOA
Mg-EG ., : Mg-EG
0.77
0.25
0.61
0.31
0.53
0.21
0.20
0.42
0.44
0.17
0.19
0.51
0.64
0.20
0.49
0.21
0.36
0.46
0.34
0.48
0.26
0.50
0.24
0.49
0.19
0.49
0.51
0.21
0.17
0.49
0.18
0.51
0.17
0.50
0.35
0.51
0.48
0.31
0.30
0.50
0.29
0.51
0.22
0.58
0.27
0.60
0.18
0.54
0.19
0.58
0.18
0.56
0.28
0.43
0.46
0.19
0.19
0.47
0.24
0.43
0.25
0.40
0.40
0.21
0.32 ■ . 0.11
0.16
0.33
0.11
0.33
0.29
0.65
0.27
0.63
0.29
0.60
. 0.45
0.43
0.40
0.45
0.45
0.50
14A
K350
0.56
. 0.51
0.46
0.41
0.47
. 0:28
0.26
0.25
0.38
0.44
0.44
0.40
0.35
0.44
. 0.31
0.25
0.29
. 0.45
0.45
0.53
0.45
0:46
0.39
0.24
0.21 .
0.31
0A4. .
0.67
0.65
0.34
0.29
0,32
. 0.26
0.22
0.21
0.36
0.47
0.35
0.34 .
0.37
0.37 .
7A
7A
K350 ■ MgEG
1.09
1.07
0.79
0.80 .
0.80
0.40
0.40
0.41
1.10
1.13
1.10
0.52
0.54
0.50
0.25
0.26
0.25
.1.00
1.03
0.97
0:68
0.70
0.68
0.16
0.21
0.18
0.73
0.86
0.84
0.30
0.30
0.28
0.18
0.16
0.15
0.44
0.47
0.47
1.23
1.20
1.20
3.5A
MgEG
3.3A
MgEG
0.81
0.84
2.09
0.88
2.09
0.86
.. 0.81
1.73
. 1:00
1.74
. 0.83
0.87
1.68
1.17
1.02
1.92
1.01
1.12
1.04
1.16
1.91
1.92
1.21
1.01
1.77
0.74
0.73
0,75
1.69
0.82
0.88 .
1.67
0.75
1,43
0.80
0.88
1.47
0.82
0.91
1.50
0.94
0.93
0.94
1.12
1.66
1.12
1.69 . 0.95
1.63
1.00
0.99
1.35
0.67
0.76.
1:33
0.67
0.78
1.35
0.64
0.68
0.73
0.70
1.53
1.55
0.76
0.86
1.50
0.76
0.77
1.75
0.97
1.14
1.16
1.73 '
1.01
1.73
0.99
1.03
1.07
1.14
1.43
1.47
0.93 . 1.12
1.45
1.26
1.14
1.10
1.37
1.06
1.15
0.97 . 1.04
1.02
1.19
0.99
1.04
0.84
1.26
1.04
0.88
1.27
1.07
0.86
0.89
1.53
0.74.
0.99
0.71
0.75
1.53
0.75
0.83
1.51
1.70
0.83
0.82
1.77
0.84
0.76
1.45
0.83
0.78
73
Table 15 (continued)
Sample
No.
17A
Mg-EG
IOA
Mg-EG
31121
0.67
0.41
'31122
0.63
0.43
31123
0.73
0.42
1.14
31131
0.77
31132
0.99
0.47
1.13
31133
0.67
1.14
0.46
31211
0.97
0.48
31212.
31213
1.10
0.48
31221
0.78
0.51
0.50
31222 . 0.64
0.65
31223
0.50
' 1.27
31231
0.50.
1.56 .
0.54
31232
31233
1.59
0.48
0.75
0.48
31311
0.84
31312
0.48
.31313
0.90
0.50
0.71
0.45
31321
0.69
0.46
31322
31323
0.60
0.49
1.28
31331
0.49
1.38
0.50
31332
31333
1.36
0.53
0.82
0.50
32111
0.94
0.75
32112
32113
0.82
0.63
0.43
32121
0.49
0.46
0.43
32122
0.58
0.41
32123
1.10
0.69
32131
1.24
. 0.52
32132
1.24
0.63 ■
32133
0.55
0.64
32211
. 0.70
0.63
32212
32213
0.82
0.66
0.56
0.40
32221 ,
0.50
0.40
32222
0.53
32223
0.42
32231
1.25
0.63
1.18
0.52
32232'
14A .
Mg-EG
0.36
0.27
0.20
1.02
0.84
0.66
0.40
0.46
0.60
0.40
0.34
0.43
0.50
0.65
0.70
0.36
0.49
■ 0.37
0.24
0.25
0.55
0.63
0.66
0.55
0.38
0.49
0.35
0.26
0.28
0,27
0.52
0.36
0.67
0.36
0.27
0.40
0.24
0.23
0.19
0.55
0.40
14A
K350
0.22
0.19
0.19
0.36
0.23
0.30
0.39
0.39
0.39
0.14,
0.16
0.37
0.48
0.40
0.43
0.47
0.36
0.43
0.15
0.28
0.16
0.29
0.25
0.22
0.25
0.41
0.27
0.19
0.17
0.18
0.27.
0.29
0.41
0.30
0.25
0.22
0.16
0.12
0.16
0.28
0.28
7A
. K350
- 7A
MgEG
3.5A
MgEG
0.90
1.38
0.87
0.93
1.36
1.09
0.85
1.39
0.91
1.08
1.03
1.40
1.11
1.79
0.82
1.75
1.10
0.83
1.54
1.44
0.84
1.55
1.05
1.46
1.55 . 1.42
.0.85
1.07
1.44
0.89
1.52
0.91
1.26
1.04
1.53
0.89
1.44
0.84
1.56
1.80
0.86
L49
0.83
1.50
1.44
1.83
0.86
1.09
1.11
1.83
0.89
0.85
1.85
1.12
0.88
1.46
0.83
1.48
0.89
0.85
1.85
0:87
0.93
0,95
1.48
0.84
0.85
0.95
1.80
1.80
0.83
0.97
0.79
1.33
1.73
1.73
0.85
1.28
1.35
' 1.77 1.00
1.50 :
0.90
0.96
1.50
0.93
0.84
1.68
0.93
0.84
1.35
1.70
0.91
1.65
1.37
0.93
1.38
1.70
0.91
0.85
1.30 ■
1.57
1.33
1.50
0.69
1.57
0.85
1.31
0.71
0.85
1.43
1.47
0.61
0.83
1.45
'0.88
. 0.59
1.70
0.96
1.50
1.67
0.78
1.50
3.3A
MgEG
0.84
0.86
0.84
0.78
0.80
0.72
0.80
0:84
0.84
.0.84
0.84
0.84
0,78
0.82
0.80
0.76
0.84
0:82
0.82 .
0.82
0.84
0.76
0.76
6.74
0.76 .
0.80
0.80
0.76
0.76
0.78
. 0.70
0.72
0.74
0.66
0.64
0.64
0.58
0.56
0.58
0.76
0.78 .
Table 15 (continued)
Sample
' No.
32233
32311
32312
32313
32321
32322
32323
32331
32332
32333
33111
33112
33113.
33121
33122
33123
33131
33132
33133
33211
33212
33213
■33221
33222
33223
33231
33232
33233
33311
33312
33313
33321
33322
33323
3333133332
33333
17A
Mg-EG
, IOA
Mg-EG
0.61
1.19
0.80
0.66
0.61
0.70
0.85
0.63 .
0.58
0.40
0.51
0.41
0.44
0.60
.0.65
1.22
1.24
0.66
0.63
1.20
0.77
0.59
0.85
0.63
0.51
1.04
0.49
0.53
0.74
0.49
0.64
. 0.40
1.62 • . 0.53
1.57 '
0.46 •
0.47
1.42
0.63
0.79
0.56
0.84
0.55
0.77
0.44
0.62
0.55
0.62
0.57
0.53
0.59
1.29
0.61
1.33
1.15
0.64
0.61
. 0.73
0.63
0.75
0.72
. 0.53
0.49
0.56
0.49
0.59
0.45
0.59
0.68 .
• 1.49
0.65
1.29
0.65
1.17
14A
Mg-EG
0.55
0.37
0.38
0.39
0.24
0.24
. 0.17
0.46
0.66.
0.69
0.36
0.28
0.44
. 0.23
0.26
0.20
0.41
0.33
0.58
0.45
0.36
0.45
0.20
0.30
0.21
0.38
0.48
0.55
0.33
0.40
0.38
0.24
0.25
0.24
0.58
0.42
0.63
14A
K350
7A
K350
7A
MgEG
0.30
1.50
. 1.38
0.39
0.30
,1.41
.0.47 ■ 1.40
1.15
0.25
0.16
. 1.18
1.18
. 0.19
1.47
0.30
0.37
1.45 .
1.47
0.30
0.31
0.49
0:42
0.52
0.52
0.39
0.43
0.17
0.43
0.24
0.42
0,21
0.49
: 0.32
0.28
0.49
0.34
0.49
0.35
0.71
0.33
0.71
0.67
0.43
0.56
0.27
0.55
0.26
0.24
0:59
0.70
0.72 '
, 0.67
0.56
0.70
0.54
0.50
0.26
0.54
0.21
0.55
0.22
0.11
0.34
0.32
0.09
0.17
0.29
0.60
0.34
0.59
0.35
0.56
0.31
1.70
1.67
1.70
1.75
1.50
1.55
1:53
. 2.13
1.75
1.75
1.13
1.15
1.15
1.17
1.21
1.50
1.19
1.21
1.45 ‘
1.20
1.41
1.21
1.50
1.25 .
1.25
1.40
1.37
1.40
1.57
1.55
1.55
1.74
1.45
1.40
1.60
1.89
1.55
3.5A
MgEG
3.3A
MgEG
0.99
0.80
0.99
0.80
0.78
0.81
1.05
0.82
0.94
0.74
0.75
0.74
0.95
0.74 .
0.78
1.01
1.04 ’ 0.82
1.05
0.84
0.61
0.82
0.74
0.86
0.76
0.84
0.80
0.92
0.80
0.87
0.83
0.96
0.74
0.88
0.76
0.79
0.75
0.77
0.75
0.82
0.71
0.82
0.82
0.79
0.92
0.81
0.85
0.90
0.83
0.86
0.67
0.96
0.85
0.98
0.83
0.96
0.87.
0.82
0.70
0.80
0.89
0.86
0.76
0.81
0.81
0.76
0.83
0.74
0.94
0.88
0.95
0.86
0.97
0.88 ,
75
Table 16. Percent Clay Mineral Composition for the Preliminary Study.
Sample
No.
SMECT
ILL
11111
11112
11113
11121
11122
11123
11131
11132
11133
11211
11212
11213
11221
11222
11223
11231
11232
11233
11311 :
11312
11313
11321
11322
11323
11331
11332
11333
12111
12)12
12113
12121
12122
12123
12131
12132
12133
12211 .
12212
12213
62
71
64
. 55 ■
51
56
63
62
63 .
61
60.
63
58
63
63
6.1
64
60
59 .
57 .
60
58 ■
59 .
58
61
64
60
60
56
60
60
63
54
. 45
48
45
61
58
63
10
09
09.
10
17 '
14
09
10
09
11
12
09
15
10
13
11
07
08
11
11
10
■12
12
12
09
10
10
09
10
09
09
. 09
10
14
12
14
10
12
10
VERM
CHLOR
KAOL
QUARTZ
00
00
00
00
01
00
00
00
00
00
00
00
01
01
01
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
01
00 .
01
12
10
11
08
07
09
11
12
10
09
11
10
07
06
05
14
. 15
16
11
12
10
06
08
07
15
12
14
12
. 16
10
09 .
07
13
22
20
20
08
11
07
11
09
12
19
17
14
11
11
11
14
13 .
14
14
13
12
10
09
11
14
15
. 15
17
. 15
15
12
11.
12
13
14
15
15
15
16
14
. 15
17
16
14
14 .
04
02
04
09
07
07 .
06
OS
08
05
03
.04
06
07
07 .
05
05
05
OS
05
05
07
06
07
04
04
05
OS
05
06
08
07
. 07
04
05
04
06 •
04,
05
76
Table 16 (continued)
Sample
No.
SMECT
12221
12222
12223'
.12231
12232
12233 .
12311
12312
12313
12321
12322
12323
12331
12332
12333
13111
13112
13113
13121
13122
13123
13131
13132
13133
13211
13212
13213
13221
13222
13223
13231
13232
13233
13311
13312
13313
13321
13322
13323
64
59 . .
60
66
67
66
61
58
60
61
61
60
69
66
68
67
67
64
62
59
57
64
69
72
59
62
62 .
64
64 •
62
69
71
'
68
58
60
• 57
62
62
61
ILL
09
10
10.
09
10
08
11
10
. io
11
■11
09
06
. 07
. 08
. 09
08
11
. 07
09
08
08
07
07
07
06
07
08
. 08
08
05
05
06
07
07
09
07
08
09
VERM
00
00
02
00
00
00
00
00
00
04
01
00
00
00
00
00
00
00
00
00
00
ob
00
00
00
00
00
.01
00
00
00
00
00
00
00
00
00
00
01
CHLOR
.
06
06
04
11
09
12
09.
13
10
04
04
08
12
12
10
10
Tl
.1 2
06
09
09
.20,
14
14
14
12
11
05
07
09
16
13
16
17 •
13
17
08
06
05
KAOL
QUARTZ
14
.17
16
11
10
10
13
13
14
14
16
15
. 09
10
10
12
11
10
17
17
17.
07
07
07
14
14
14
14
16
16
08
08
07
13
13
12
17
. 17
17
06
08
07
04
03
04
05
05
06
06
07
07
. .04
05
05
. 02 .
02 03
08
06
08
01
02
01
06
06
06
05
06
.0 6
03
03
02
05
07 .
05 .
06
07
0.7
.
77
Table 16 (continued)
Sample
No.
SMECT
13331
13332
13333
21111
21112
21113
21121
21122
21123
21131
21132
21133
21211
21212
21213
21221
21222
21223
21231
21232
21233
21311
21312
21313
21321
21322
21323
21331
21332
21333
22111
22112
22113
22121
22122
22123
22131
22132
22133
67
70
72
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
ILL
08
06
OS
41
39
37
33
35
36
37
35
41
35
39
39
43
41
41
37
43
39
30
35
37
38
37
38
48
48
43
57
41
42
41
40
40
. 42
40
42
VERM
CHLOR
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
13
11
10
26
24
23
14
14
14
25
28
28
21
21
21
10
11
10
21
21
21
19
16
15
11
13
11
18
16
14
14
18
14
08
10
08
19
20
19
KAOL
10
10
10
29
30
33
37
37
37
30
29
26
32
33
31
36
37
36
33
29
33
38
37
36
39
37
. 38.
29
31
34
28
33
35
42
40
41
34
32
31
QUARTZ
03
03
03
04
07
06
15
15
13
08
08
05
11
08
09
11
11
13
10
07
07
12
13
12
11
13
13
OS
OS
08
01
08
09
09
11
11
05
07
08
78
Table 16 (continued)
Sample
No.
SMECT
22211
22212
22213
22221 •
22222
22223
22231
22232
22233
22311
22312
22313
22321
22322
22323
22331
22332
22333
23111
23112
23113
23121
23122
23123
23131
23132
23133
23211
23212
23213
23221
23222
23223
23231
23232
23233
23311
23312
23313
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
ILL
VERM
42
36
40
40
40
39
44
47
41
39
35
35
39
45
39
39
39
40
42
43
41
39
41
41
44
. 42
42,
43:
45
48
42
45
43
35
34
35
' 38
39
39
00
00
00 ,
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
CHLOR
KAOL
QUARTZ
21
18
22
09
09
10
16
17
17
17
17
19
11
09
10
16
18
17
17
15
18
12
10
12
19
20
23
19
18
16
09
08
12
18
25
24
15
14
15
30
35
30
38
38
38
33
32
35
32
36
33
37
34
38
37
34
33
30
32
30
33
34
34
29
29
29
32
30
30
34
33
33
29
27
27
30
28
29
07
11
09
13
13
13
06
04
07
11
12
14
14
12
13
08
09
10
11
10
11
15
15
13
08
09
07
07
08
06
14
14
12
17
14
15
16
18
17
79
Table 16 (continued)
Sample
No.
SMECT
23321
23322
23323
23331
23332
23333
31111
31112
31113
31121
31122
31123
31131
31132
31133
31211
31212
31213
31221
31222
31223
31231
31232
31233
31311
31312
31313
31321
31322
31323
31331
31332
31333
32111
32112
32113
32121
32122
32123
00
00
00
00
00
00
'15
16
18
14
13
15
15
15
16.
20
17
18
14
12
12
21
22
24
13
14
15
14
14
10
20
20
20
14
14
13
11
10
12
ILL
35
36
39
49
48
49
30
32
31
33
' 36
36
39
28
38
32
33
31
37
38
36
33
30
27
33
32
33
37
37
33
30
29
31
35
44
41
37
37
33
VERM
,
00
00
00
00
00
00
04
01
OS
06
03
00
17
18
10
00
02
07
09
07
02
01
07
08
00
04
00
04
00
13
11
12
10
. os
02
03
03
OS
. 04
CHLOR
14
12
12
13
18
14
12
13
13
09
08
08
09
07
09
14
14
13
OS
06
13
16
11
13
16
12
14
06
11
05
09
07
07
09
12
09
08
07
07
KAOL
34
35
31
29
29
31
30
31
25
28
28
29
18
26
25
25
25
23
26
29
28
23
. 25
21
31
30
31
30
29
.31
23.
26
27
30
' 25
29
32
32
34
QUARTZ
16
17
18
09
05
06
09
07
08
11 .
11
11
03
07
03
08
08
08
08
09
08
07
06
07
07
08
07
10
09
. 08
.06
06
OS
07.
03.
OS
09 .
09
10
80
Table 16 (continued)
Sample
No.
32131
32132
32133
32211
32212
32213
32221
32222
32223
32231
32232
32233
32311
32312
32313
32321
32322
32323
32331
32332
32333
33111
33112
33113
33121
33122
33123
33131
33132
33133
33211
33212
33213
33221
33222
33223
33231
33232
33233
SMECT
16
21
17
12
13
14
13
12
09
18
19
18
13
12
13
13
11
13
17
17
17
14
15
19
11
05
13
. 26
27
22
14
15
14
12
12
.11
18
20
17
ILL
VERM
CHLOR
KAOL
QUARTZ
41
35
36
41
46
44
37
37
47
37
34
36
43
41
39
35
36
38
36
36
35
44
44
37
42
40
33
34
32
30
44
40
40
35,
43 ;
46
34
36
38
07
02
07
02
01
06
04
05
01
08
04
07
00
03
00
00
03
00
05
08
11
02
00
02
03
01
00
03
02
08
03
01
01
00
02
00
00
00
00
08
10
12
11
09
07
07
06
07
08
09
09
13
10
15
11
07
08
08
10
08
12
15
14
07
10
09
10
10
11
12
12
16
11
10
10
21
17
16
25
27
24
29
28
26
33
34
32
25
27
25 .
27
29
27
33
34
33
30
24
24
21
20
21
25
25
31
19
21
23
21
25
22
30
24
.25,
20
20
21
03
05
04
05
03
02
06.
06
04
04
06
05
05
05
OS
09
09
.0 9
04
OS
OS
07
07
08
12
10
14
08
08
07
06
07
07
12
09 .
09
07
08
07
81
Table 16 (continued)
Sample
No.
SMECT
ILL
VERM
CHLOR
33311
33312
33313
33321
33322
33323
33331
33332
33333
13
13
13
11
12
13
20
18
17
42
42
38
38
40
39
37.
37
37
02
06
06
05
07
03
07
02
09
09
07
08
04
04
07
07
09
10
KAOL
27
26
28
34
30
38
. 22
27
22
QUARTZ
06
05
08
08
08
09
09
05
06
82
Table 17. ANOVA for Main Effects on the 17A Peak (MgEG) for All Three Soils StudiedPreliminary Study
Soxirce
Total
Soils
Clay Sep.
Slide
Field/Slide
Error
Degrees of
Freedom
Sum of
Squares
242
2
6
18
54
162
1108.160
972.767
3.739
24.946
96.770
9.937
Mean
Squares
4.579
. 486.383
0.623
1.386
1.792
0.061
Variance
Component
6.635
5.997
-0.028
-0.045
0.577
0.061
F-Value
780.43*
0.45
0.77
29.21*
* - significant at a = 0.05
Table 18. ANOVA for Main Effects on the IOA Peak (MgEG) for AU Three Soils StudiedPreliminary Study
Source
Total
Soils
Clay Sep.
Slide .
Field/Slide
Error
*
Degrees of
Freedom
Sumof
Squares
Mean
Squares
Variance
Component
242
2
6
18
54
162
8.243
6.294
0.233
0.336
1.028
0.353
0.034
3.147
0.039
0.019
0.019
0.002
0.047
0.038
0.001
0.000
0.006
0.002
F-Value
81.14*
2.08
0.97
8.77*
- significant at a = 0.05
I
83
Table 19. ANOVA for Main Effectsonthe 14A Peak (MgEG) for AU Three SoUs Studied—
PreUminary Study
Source
Total
Soils
Clay Sep.
SUde
Field/SUde
Enor
Degrees of
Freedom
242
2
6
18
54
162
Sum of
Squares
Mean
Squares
Variance
Component
4.991
2.043
0.375
0.106
1.854
0.613 .
0.021
1.021
0.063
0.006
0.034
0,004
0.028
0.012
0.002
-0.003
0.010
0.004
F-Value
16.34*
10.64*
0.17
9.07*
* - significant at a = 0.05
Table 20. ANOVA for Main Effects on the 14A Peak (K350) for AU Three SoUs Studied—
PreUminary Study
Source
Total
Soils
Clay Sep.
SUde
Field/SUde
Enor
Degrees of
Freedom
242
2
6
18
54
162
* - significant at a = 0.05
Sumof
Squares
5.170
0.550 *
0.089
0.451
3.534
0.545
Mean
Squares
Variance
Component
0.021
0.275
0.015
0.025
0.065
0.003
0.027
0.003
0.000
-0.004
0.021
0.003
F-Value
18.45*
0.59
0.38
19.45*
84
Table 21. ANOVA for Main Effects on the 7A Peak (MgEG) for All Three Soils StudiedPreliminary Study
Source
Total
Soils
Clay Sep.
Slide
Field/Slide
Error
Degrees of
Freedom
Sum of
Squares
Mean
Squares
Variance
Component
242
2
6
18
54
162
134.659
20.615
2.835
5.903
4.259
1.047
0.143
10.307
0.472
0.328
0.079
0.006
0.185
0.121
0.005
0.028
0.024
0.006
F-Value
21.82*
1.44
4.16*
12.20*
* - significant at a = 0.05
Table 22. ANOVA for Main Effects on the 7A Peak (K350) for All Three Soils StudiedPreliminary Study
Source
Total
Soils
Clay Sep.
Slide
Field/Slide
Error
Degrees of
Freedom
242
2
6
18
54
162
* - significant at a = 0.05
Sum of
Squares
Mean
Squares
Variance
Component
44.365
20.073
10.450
4.087
9.594
0.162
0.183
10.036
1.742
0.227
0.178
0.001
0.224
0.102
0.056
0.005
0.059
0.001
F-Value
5.76*
7.67*
1.28
177.52*
85
Table 23. ANOVA for Main Effects on the 3.5 A Peak (MgEG) for All Three Soils StudiedPreliminary Study
Source
Degrees of
Freedom
Total
Soils
Clay Sep.
Slide
Field/Slide
Error
242
2
6
18
54
162
Sum of
Squares
Mean
Squares
Variance
Component
12.311
7.397
0.351
2.137
1.711
0.714
0.051
3.698
0.059
0.119
0.032
0.004
0.068
0.045
-0.002
0.100
0.009
0.004
F-Value
63.14*
0.49
3.75*
7.19*
* - significant at a = 0.05
Table 24. ANOVA for Main Effects on the 3.3 A Peak (MgEG) for All Three Soils StudiedPreliminary Study
Source
Total
Soils
Clay Sep.
Slide
Field/Slide
Error .
*
„
Degrees of
Freedom
Sum of
Squares
242
2
6
18
54
162
10.449
5.913
1.046
1.441
1.734
0.315
significant at a = 0.05
Mean
Squares
0.043
2,956
0.174
0.080
0.032
0.002 .
Variance
Component
0.055
0.034
0.003
0.005
0.010
0.002
F-Value
16.96*
2.18
2.49*
16.49*
86
Table 25. ANOVA of Percent Smectite Composition for All Three Soils Studied—Prelimi­
nary Study
Source
Total
Soil
Clay Sep.
Slide
Field/Slide
Error
*
Degrees of
Freedom
Sum of
Squares
Mean
Squares
Variance
Component
242
2
6
18
54
162
16.925
16.596
0.034
0.055
0.201
0.039
0.070
8.298
0.006
0.003
0.004
0.000
0.104
0.102
0.000
0.000
0.001
0.000
F-Value
1463.49*
1.85
0.82
15.28*
- significant at a = 0.05
Table 26. ANOVA of Percent Illite Composition for All Three Soils Studied—Preliminary
Study
Source
Total
Soil
Clay Sep.
Slide
Field/Slide
Error
Degrees of
Freedom
Sum of
Squares
Mean
Squares
Variance
Component
242
2
6
18
54
162
5.003
4.656
0.077
0.019
0.158
0.093
0.021
2.328
0.013
0.001
0.003
0.001
0.030
0.029
0.000
0.000
0.001
0.001
* - significant at a = 0.05
F-Value
180.88*
11.92*
0.37
5.09*
87
Table 27. ANOVA of Percent Vermiculite Composition for All Three Soils Studied—Pre­
liminary Study
Source
Total
Soil
Clay Sep.
Slide
Field/Slide
Error
Degrees of
Freedom
Sum of
Squares
Mean
Square
. Variance
Component
242
2
6
18
54
162
0.219
0.090
0.015
0.012
0.059
0.043
0.001
0.045
0.002
0.001
0.001
0.000
0.001
0.001
0.000
0.000
0.000
0.000
F-Value
18.58*
3.55*
0.63
4.06*
* - significant at a = 0.05
Table 28. ANOVA of Percent Chlorite Composition for All Three Soils Studied—Prelimi­
nary Study
Source
Total
SoU
Clay Sep.
SUde
Field/SUde
Error
Degrees of
Freedom
Sum of
Squares
Mean
Squares
Variance
Component
242
2
6
18
54
162
0.579
0.185
0.019
0.067
0.261
0.047
0.002
0.093
0.003
0.004
0.005
0.000
0.003
0.001
0.000
0.000
0.001
0.000
* - significant at a = 0.05
.
F-Value
29.77*
0.83
0.77
16.66*
88
Table 29. ANOVA of Percent Kaolinite Composition for All Three Soils Studied—Prelimi­
nary Study
Source
Total
Soil
Clay Sep.
Slide
Field/Slide
Error
Degrees of
Freedom
242
2
6
18
54
162 '
Sum of
Squares
Mean
Square
Variance
Component
1.987
1.693
0.051
0.027
0.172
0.044
0.008
0.847
0.009
0.001
0.003
0.000
0.012
0.010
0.000
0.000
0.001
0.000
F-Value
99.01*
5.65*
0.47
11.68*
* - significant at a = 0.05
Table 30. ANOVA of Percent Quartz Composition for AU Soils Studied—Preliminary Study
Source
Total
Soil
Clay Sep.
Slide
Field/Slide
Error
Degrees of
Freedom
242
2 ■
6
18 .
54
162
* - significant at a = 0.05
Sum of
Squares
Mean
Squares
Variance
Component
0.291
0.114
0.021
0.016
0.119
0.021
0.001
0.057
0.003
0.001
0.002
0.000
0.001
0.001
0.000
0.000
0.001
0.000
F-Value
16.06*
4,06*
0.40
17.03*
Table 3 1. Complete Peak Area Measurements (in.2) for the Main StudySample
No.
17AMgEG
11
12
21
22
31
32
41
42
SI
52
61
62
71
72
SI
82
91
92
IOl
102
II I
.112
121
122
131
132
141
142
151
4.45
5.65
2.40
2.50
1.39
2.09
2.07
1.85
5.17
2.89
8.56
4.27
15.53
7.20
5.04
3.19
0.93
0.91
0.35
1.21
0.22
0.51
0.13
0.31
0.00
0.00
4.61
4.10
5.52
IOAMgEG
0.35
0.38
0.39
0.33
0.23
0.28
0.14
0.12
0.09
0.06
. 0.22
0.14
0.28
0.16
0.81
0.46 0.79
0.68
0.53
0.84
0.99
0.89
1.21
0.72
1,01
0.71
0.40
0.38
0.14
HAMgEG
I4AK350
0.52
0.60
0.59
0.34
0.19
0.19
0.21
0.18
0.25
0.17
0.72
0.30
0.00
0.35
1.29
0.63
0.42
0.60
0.20
0.69
0.31
0.49
0.31
0.49
0.35
0.35
0.35
0.22
0.35
0.59
0.62
0.41
0.49
0.42
0.54
0.44
0.52
0.33
0.48
0.66
0.62
0.75
0.59
0.90
0.63
0.80
0.88
0.69
0.61
0.89
0.60
0.59
0.69
0.72
0.58
0.42
0.47
0.55
7AK350 7AK500 7AMgEG
0.18
0.26
0.27
0.48
0.25
0.27
0.39
0.18
0.73
0.21
0.39
0.47
0.22
0.13
0.29
0.28
0.45
0.53
0.46
0.44
0.57
2.11
1.83
1.54
1.64
1.65
0.36
0.44
0.14
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.14
0.00
0.00
0.00
0.73
0.65
0.63
0.36
0.36
0.48
0.43
0.59
0.61
0.60
1.38
0.76
1.01
0.66
2.00
1.32
1.98
1.85
1.32
1.50
2.51
2.73
3.20
1.80
2.81
2.55
0.72
0.55
0.44
3.5A MgEG
3.3AMgEG
0.47
0.41
0.43
0.37
0.38
0.47
0.44
0.67
0.58
0.61
0.54
0.36
0.50
0.33
0.42
0.56
0.55
0.73
0.65
1.10
0.72
0.62
0.78
1.08
0.91
0.87
0.85
1.04
0.74
1.32
0.75
0.53
0.38
0.44
0.23
0.33
0.59
0.52
0.37
1.20
0.71
0.91
1.31
1.05
1.01
1.35
1.40
1.76
1.20
2.24
1.15
0.50
0.36
0.27
Table 31 (continued)
Sample
No.
17AMgEG
IOAMgEG
152
161
162
171
-172
181
182
191
192
201
202
211
212
221
222
231
232
241
. 242
251
252
261
262
271
272
281
282
291
292
0.17
0.11
0.19
0.11
0.28
0.16
0.35
0.19
0.38
0.57
0.63
0.60
. 0.95
0.28
0.53
0.22
0.16
0.12
0.11
0.34
0.30
0.50
0.52
0.87
0.88
1.51
1.33
1.59
1.50
6.80
4.51
14.61
6.30
15.93
2.68
13.30
2.57 .
16.40
8.30
7.57
6.25
9.71
2.59
11.00
8.50
4.59
11.00
3.22
8.50
6.70
8.90
8.28
8.87
8.16
1.22
1.57
0.00
0.00
14AMgEG 14AK350
O.O0
0.00
0.00
0.00
O.O0
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.18
0.63
0.41
0.23
0.41
1.17
0:52
0.65
0.79
- 0.78
0.70
0.68
0.84
1.15
1.31
0.91
1.24
1.08
0.68
1.13
0.68
0.79
0.73
0.99
1.01
1.20
1.07
0.80
0.74
0.92
0.69
0.13
0.21
7AK350
0.12
0.19
0.24
0.21
0.22
0.16
0.11
0.13
0.13
0.00
0.00
0.12
0.00
0.60
0.14
0.53
0.16
0.34
0.16
0.19
0.08
0.13
0.15
3.60
2.84
0.82
1.05
4.72
5.63
7AK500 7AMgEG
0.00
0.00.
0.00
0.00
0.00
0.00
0.00
0.00
o.oo
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.41
0.29
0.42
0.22
0.55
0.15
0.48
0.23
0.51
0.87
0.93
0.97
1.01
0.49
1.01 .
0.52
0.38
0.39
0.29
0.79
0.95
1.02
1.33
4.13
4.16
3.30
3.24
5.59
5.06
3.5A MgEG
3.3A MgEG
0.27
0.30
0.21
0.21
0.35
. 0.27
0.34
0.37
0.70
0.54
0.55
1.06
0.46
1.03
0.68
0.88
1.03
0.65
1.17
0.87
0.72
0.99
0.75
0.63
0.77
0.74
0.62
0.62
0.44
0.71
1.21
0.91
2.10
1.90
1.47
1.15
0.35
0.61
0.43
0.73
0.65
0.45
0.67
0.47
0.46
0.71
2;03
2.11
2.36
2.62
3.78
3.13
Table 31 (continued)
Sample
No.
17AMgEG
301
302
311
312
321
322
331
332
341
342
351
352
361
362
371
372
381
382
391
392
401
402
411
412
421
422
431
432
441
0.00
0.00
0.00
0.00
0.00 .
0.00
0.00
0.00
0.00
0.00
0.00
0.00 „
0.00'
0.00
0.00
0.00
8.53
8.45
6.60
5.00
5.85
5.12
5.82
6.24
0.95
. 1.27
0.00
0.00
ODQ
IOAMgEG
LlO
0.57
1.37
1.61
2.03
2.05
1.65
1.91
1.97
1.92
1.15
0.76
1.69
1.40
1.20
1.29
0.62
0.58
0.88
0.69
0.44
0.53
0.53
0.63
1.26
1.11
1.30
1.58
1.34
14AMgEG 14AK350
0.00
0.00
0.00
0.00
0.44
0:62
0.39
0.49
0.56
0.54
0.00
0.00
0.00
0.44
0.00
0.00
0.00
0.00
0.95
1.05
0.00
0.00
0.80
0.96
0.45
0.45
0.48
0.41
0.43
0.00
. 0.16
0.23
0.21
0.49
0.61
0.58
0.71
0.56
0.66
0.00
0.00
0.00
0.28
. 0.00
0.22 •
0.55
0.49
0.54
0.81
0.45
0.31
0.34
0.30
0.49
0.34
0.40
0.41
0.57
7AK350
4.63
2.46
0.94
1.79
2.10
2.97
2.03
2.53
3.25
1.24
1.67
0.68
3.97
1.12
1.04
0.81
0.79
0.61
0.42
0.49
0.20
. 0.23
0.11
0.32
1.15
1.69
3.36
0.96
3.13
7AK500 TAMgEG.
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
6.06
2.44
5.03
4.59
3.03
3.56
3.63
3.75
3.47
3.22
2.23
1.93
5.22
4.69
4.78
4.95
1.44
1.33
1.65
1.60
0.82
0.92
0.89
0.97
2.40
2.43
2.66
2.60
3.97
3.5AMgEG
3.3A MgEG
3.19
1.38
2.59
2.64
2.15
2.05
2.31
2.07
1.91
2.11
1.42
1.03
2.75
2.69
2.49
2.41
1.03
0.94
1.49
1.31
0.55
0.48
0.49
0.73
1.43
1.33
1.61
1.39
2.15
0.73
0.35
1.20
1.09
1.91
1.61
1.60
1.54
1.53
1.33
0.89
0.71
1.00
1.11
0.89
0.90
1.40
1.13
1.51
1.67
0.47
0.56
0.58
0.69
1.19
1.10
1.24
1.00
1.07
Table 31 (continued)
Sample
No.
17AMgEG
442
451
452
461
462
471
472
481
482
491
492
501
502
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1.53
2.27
IOAMgEG
14AMgEG
14AK350
7AK350
1.40
0.64
0.68
0.84
0:77
1.21
1.00
1.30
1.28
1.35
1.39
0.70
0.90
0.48
0.00
0.00
0.57
0.55
0.62
0.58
0.63
0.54
0.54
0.54
0.00
0.00
0.54
0.00
0.18
0.81
0.71
0.49
0.54
0.56
0.41
0.45
0.59
0.39
0.27
2.63
0.29
0.24
1.13
1.56
4.25
4.06
4.06
2.33
1.14
0.87
0.10
0.14
7AK500 7AMgEG
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
3.81
1.90
1.90
7.40
7.60
7.50
7.25
6.55
6.35
3.59
4.25
1.75
2.21
3.5A MgEG
3.3A MgEG
2.06
1.24
1.21
4.63
4.03
5.37
3.80
4.59
3.75
2.81
2.81
1.65
1.57
1.08
0.95
1.01
0.86
0:80
1.45
1.10
1.39
1.20
1.37
1.52
1.69
1.76
VO
to
93
Table 32. Complete Data Table for Modification IV
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
PSM
PIL
PVM
PCA
PKA
PQU
ECEC
LCEC
TKIL8
54.3
39.7
35.2
43.3
58.9
57.3
70.1
34.4
9.6
9.0
3.2
1.6
0.0
51.3
67.4
75.6
72.3
72.8
37.7
48.7
46.8
59.0
57.6
47.6
54.5
52.0
36.0
12.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
53.2
33.7
52.6
15.7
22.6
21.2
10.7
4.7
6.7
5.7
21.0
30.9
33.3
34.3
36.7
33.0
19.6
7.6
4.3
5.5
8.1
15.2
17.5
21.0
12.6
8.1
6.6
11.1
14.2
16.3
35.0
35.1
28.6
37.0
50.2
44.3
49.5
46.9
36.0
33.0
16.0
20.5
20.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 .
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.9
0.0
0.0
0.0
0.0
0.0
0.0
3.5
0.0
0.0
0.0
0.0
13.1
14.1
18.3
17.1
12.7
12.4
9.2
13.2
17.7
16.2
13.4
12.7
12.6
11.3
11.6
13.1
11.8
9.1
27.2
17.9
14.8
12.8
18.8
24.3
16.7
15.8
7.2
10.1
1.7
2.2
2.7
7.4
8.0
7.7
0.0
2.4
1.4
6.9
7.6
7.8
15.0
2.0
5.6
17.9
17.1
8.2
7.1
21.7
18.7
5.0
19.3
4.1
3.7
11.1
3.7
27.8
1.6
40:2
35.0
6.3
47.6
1.4
47.3 . 1.7
3.6
50.7
15.8
1.9
3.5
10.2
2.2
4.7
5.4
4.9
5.6
4.5
10.7
9.2
13.1
2.8
3.4
13.9
3.5
12.0
5.9
9.6
10.8
10.7
14.6
3.1
1.5
16.4
1.8
38.6
5.4
37.3
0.8
60.4
0.0
69.2
0.5
59.7
1.9
40.5
1.5
46.1
42.5
0.2
51.9
1.1
0.2
57.9
0.0
65.2
5.4
18.4
6.5
31.5
1.5
18.0
62.70
50.43
46.62'
52,18
64.88
63.71
74.85
45.18
25.03
24.36
19.02
17.76
15.52
60.36
73.02
80.37
77.17
77.64
49.25
58.65
56.98
66.38
65.20
56.38
62.69
60.85
45.05
26.51
17.30
13.24
14.71
17.68
16.81
17.72
15.90
20.46
13.91
60.52
43.43
61.08
56.25
47.50
42.50
42.50
51.25
46.25
62.50
32.50
21.25
20.00
20.00
17.50
17.50
40.00
58.75
72.50
62.50
63.75
42.50
48.75
43.75
48.75
46.25
53.75
47.50
37.50
28.75
22.50
17.50
12.50
17.50
12.50
12.50
10.00
23.75
17.50
17.50
47,40
42.50
47.50
15
15
14
13
8
11
8
20
27
30
27
27
29
19
14
11
11
17
19
20
23
22
17
15
18
26
22
29
24
21
23
37
38
33
27
24
24
19
22
20
.
Table 32 (continued)
41
42
43
44
45
46
47
48
49
50
PSM
PIL
PVM
49.6
9.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
14.3
19.0
40.3
47.6
38.0
35.9
16.1
20.6
26.4
37.2
30.2
9.1
0.9
0.0
0.0
0.0
0.0
0.6
1.0
0.0
0.0
PCA
PKA
PQU
ECEC
LCEC
TKIL8
5.3
6.3
7.2
7.7
6.0
7.6
5.2
4.9
6.9
7.0
15.3
41.7
44.1
53.9
51.6
75.1
71.1
66.0
53.0
37.6
1.6
1.6
1.1
0.3
6.5
1.1
2.5
1.7
2.8
10.9
72.95
25.71
17.24
15.76
14.72
11.97
13.24
14.99
15.33
26.85
38.75
17.50
12.50
12.50
31.25
20.00
17.50
17.50
12.50
30.00
21
30
33
33
23
19
20
20
34
24
95
Table 33. Complete Data Table for Modification V
PSM
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
47.2
33.7
30.0
35.6
49.8
48.0
63.2
26.9
6.9
6.7
2.2
1.1
0.0
44.3
61.2
72.2
68.5
68.9
34.6
43.0
41.2
52.7
52.5
42.9
47.6
44.7
26.0
8.9
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0:0
0.0
44.9
25.7
44.6
PIL
13.7
19.2
18.2
8.8
3.9
5.6
5.2
16.4
22.0
24.8 .
23.2
24.9
22.0
16.9
6.7
4.1
5.2
7.7
13.9
15.5
18.5
11.3
. 7.4
6.0
9.8
12.3
11.8
25.4
21.9
16.9 .
23.2
35.7
30.3
34.7
30.9
22.8
20.2
13.5
15,6
16.9
PVM
PCA
PKA
PQU
ECEC
LCEC
TKIL8
0.0
0.0
0.0
11.3
12.0
15.6
14.1
10.6
10.4
8.2
10.3
12.6
11.9
9.1
8.6
8.3
. 9.7
10.5
12.6
11.2
8.6
24.9
15.8
13.0
11.5
17.1
21.9
14.6
13.6
5.1
7.3
1.0
1.3
1.7
5.2
5.5
5.4
0.0
1.5
0.8
5.8
5.7
6.6
26.0
30.3
29.2
35.6
31.3
32.4
20.1
43.5
57.4
51.9
64.5
64.2
67.3
27.2
18.5
9.0
10.3
10.6
16.8
23.1
24.3
21.5
17.4
19.3
25.4
28.1
55.7
54.3
75.3
81.8
74.7
57.6
63.1
59.7
68.3
73.4
78.9
31.2
47.9
30.4
1.7
4.7
7.0
5.8
4.2
3.5
3.3
2.8
LI
4.7
1.0
1.2
2.4
1.7
3.1
2.1
4.7
4.2
9.8
2.5
3.0
3.1
5.4
9.8
2.6
1.3
1.3
3.9
0.5
0.0
0.3
1.3
1.0
0.1
0.7
0.1
0.0
4.5
5.0
1.3
55.58
44.07
40.93
44.33
56.04
54.68
68.23
37.12
20.17
20.17
15.47
14.63
13.01
53.23
67.04
77.14
73.58
73.91
45.84
52.76
51.08
60.18
60.19
51.67
55.81
53.49
34.71
21.52
13.79
11.11
12.22
14.89
14.03
14.83
13.22
15.88
11.58
52.32
34.97
52.95
56.25
47.50
42.50
42.50
51.25
46.25
62.50
32.50
21.25
20.00
20.00
17.50
17.50
40.00
58.75
72.50
62.50
63.75
42.50
48.75
43.75
48:75
46.25
53.75
47.50
37.50
28.75
22.50
17.50
12.50
17.50
12.50
12.50
10.00
23.75
17.50
17.50
47.40
42.50
47.50
15
15
14
13
8
11
8
20
27
30
27
27
29
19
14
11
11
17
19
20
23
22
17
15
18
26
22
29
24
21
23
37
38
33
27
24
24
19
.22
20
0:0
0.0
0.0
0.0
o:o
0.0
0.0
o:o
0.0
0.0
o.o
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
o,o
0.0
0.0
1.2
0.0
0.0
0.0
0.0
0.0
0.0
2.3
0.0
0.0
0.0
0.0
96
Table 33 (continued)
41
42
43
44
45
46
47
48
49
50
PSM
PIL
PVM
PCA
PKA
PQU
ECEC
LCEC
TKIL8
43.1
6.4
0.0
0.0
0.0
0.0
0.0
0.0
0.0
10.4
16.5
28.5
33.1
24.7
23.6
9.2
12.0
15.9
24.3
22.0
7.9
0.7
0.0
0.0
0.0
0.0
0.3
0.6
0.0
0.0
4.6
4.5
4.9
5.0
3.9
4.3
3.0
3.0
4.5
5.1
26.6
58.9
61.2
70.1
68.0
85.8
83.1
79.5
69.3
54.5 .
1.4
1.1
0.8
0.2
4.3
0.6
1.4
1.0
1.9
7.9
64.27
20.60
14.41
13.04
12.42
10.28
11.07
12.16
12.81
21.71
38.75
17.50
12.50
12.50
31.25
20.00
17.50
17.50
12.50
30.00
21
30
33
33
23
19
20
20
34
. 24
97
Table 34. Complete Data Table for Modification IX.
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
PSM
PIL
PVM
PCA
PKA
PQU
ECEC
LCEC
48.6
34.5 '
30.3
37.9
59.3
51.8
65.3
29.5
7.8
7.4
2.6
1.3
0.0
45.8
62.3
71.3
67.6
68.1
32.7
43.2
41.4
53.5
52.1
42.1 ,
49.0
46.5
31.0
10.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
OO
47.6
28.9
47.0
17.7
24.6
22.8
11.7
5.7
7.5
6.7
22.5
31.4
34.0
34.5
36.8
33.0
21.8
8.6
5.0
6.4
9.5
16.4
19.3
23.2
14.3
9.1
7.3
12.5
15.9
17.5
35.9
35.1
28.6
37.0
50.2
44.2
49.5
46.9
36.0
33.3
17.9
22.0
22.4
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.9
0.0
0.0
0.0
0.0
0.0
0.0
3.5
0.0
0.0
0.0
0.0
14.6
15.4
19.7
18.8
13.8
14.0
10.6
14.1
18.0
16.5
13.5
12.7
12.6
12.5
13.4
15.5
13.7
10.6
29.4
19.8
16.3
14.6
21.2
26.8
18.7
17.7
7.7
10.4
1.7
2.2
2.7
7.4
8.0
. 7.7
0.0
2.4
1.4
7.7
8.1
817
16.8
19.4
18.4
23.8
17.5
21.9
12.9
29.9
41.0
35.7
47.9
47.5
50.7
17.6
11.8
5.6
6.3
6.5
9.9
14.6
. 15.4
13.6
10.9
. 11.8
16.3
18.3
41.6
38.2
60.4
69.2
59.7
40.5
46.1
42.5
51.9
57.9
65.2
20.6
33.8
20.0
2.2
6.1
8.8
7.8
3.7
4.7
4.3
3.9
1.6
6.4
1.4
1.7
3.6
2.1
4.0
2.6
5.8
5.2
11.6
3.1
3.7
4.0
6.7
11.9
3.4
1.7
2.0
5.6
0.8
0.0
0.5
1.9
1.5
0.2
1.1
0.2
0.0
6.0
7.0
1.7
58.11
46.18
42.52
47.62
65.65
59.08
70.81
41.12
23.54
23.00
18.52
17.51
15.52
55.86
68.81
76.93
73.31
73.75
45.17
54.18
52.58
61.89
60.70
51.81
58.18
56.33
40.75
24.72
17.30
13.24
14.71
17.68
16.81
17.72
15.90
20.46
13.91
55.79
39.34
56.48
56.25
47.50
42.50
42.50
51.25
46.25
62.50
32.50
21.25
20.00
20.00
17.50
17.50
40.00
58.75
72.50
62.50
63.75
42.50
48.75
43.75
48.75
46.25
53.75
. 47.50
.37.50
28.75
22.50
17.50
12.50
17.50
12.50
12.50
10.00
23.75
17.50
17.50
47.40
42.50
47.50
TKIL8
15
15
14
13
8
11
8
20
27
30
27
27
29
19
14
11
11
17
19
20
23
22
17
15
18
26
22
29
24
21
23
37;
38
33
27
24
24
19
22
20
98
Table 34 (continued)
41
42
43
44
45
46
47
48
49
50
PSM
PIL
PVM
PCA
PKA
PQU
ECEC
LCEC
TKIL8
44.0
7.9
0.0
0.0
0.0
0.0
0.0
0.0
0.0
11.8
21.2
41.0
47.6
38.0
35.9
16.1
20.6
26.4
37.2
31.2
10.1
1.0
0.0
0.0
0.0
0.0
0.6
1.0
0.0
0.0
5.9
6.5
7.2
7.7
6.0
7.6
5.2
4.9
6.9
7.2
16.9
42.5
44.1
53.9
51.6
75.1
71.1
66.0
53.0
38.6
1.9
1.6
1.1
0.3
6.5
1.1
2.5
1.7
2.8
11.1
69.95
24.47
17.24
15.76
14.72
11.97
13.24
14.99
15.33
24.72
38.75
17.50
12.50
12.50
31.25
20.00
17.50
17.50
12.50
30.00
21
30
33
33
23
19
20
20
34
24
99
Table 35.. Complete Data Table for Modification X
PSM
PIL
15.1
I
41.7
2
20.6
28.9
25.6
19.3
3
4
30.8
9.5
5
50.5
4.9
6
42.5
6.1
5.9
7
57.9
22.7
8
17.3
22.3
9
5.6
5.5
25.0
10
11
1.7
23.3
0.8
25.0
12
0.0
22.0
13
18.5
14
38.9
55.8
7.6
15
67.5
4.8
16
63.6 . 6.0
17
63.9
18
8.9
29.7
14.9
19
37.7
.16.9
20
20.1
21 . 35.9
12.6
22
47.1
23
47.0
8.2
6.5
37.7
24
10.8
25
42.2
13.4
39.3
26
12.4
22.0
27
28
7.2
25.9
0.0
21.9
29
30
0.0
16.9
23.2
0.0
31
35.7
32
0.0
0.0
30.3
33
0.0
34.7
34
35
30.9
0.0
22.8
0.0
36
0.0
20.2
37
38
39.5
14.8
16.4
21.7
39
39.2
18.6
40
PVM
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1,2
6,0
0.0
0.0
0.0
0.0
0.0
2.3
0.0
0.0
0.0
0.0
PCA
12.5
12.9
16.6
15.2
11.7
11.5
. 9.5
10.9
12.8
...
12.1
9.1
8.6
8.3
10.7
11.9
14.7
13.0
10.0
26.7 .
17.4
14.1
12.8 '
19.2
23.9
16.0
15.0
5.4
7.5
1.0
1.3
1.7
5.2
5.5
5.4
0.0
1.5
* 0.8
6.4
6.1
7.3
ECEC
LCEC
TKIL8
50.95
28.7
1.9
5.0
40.01
32.5
7.4
37.17
31.0
6.3
38.3
40.1 i
57.10
29.8
3.1
3.8
49.92
35.9
3.8
63.66
22.9
. 3.0
33.49
46.0
19.05
1.1
58.2
4.7
52.6
19.09
15.07
1.0
64.8
1.2
14.43
64.2
2.4
13.01
67.3
1.8
48.65
29.9
3.6
62.44
21.1
2.5
73.27
10.5
5.4
69.43
11.9
69.71
4.9
12.3
41.76
18.1 , 10.6
2.7
48.39
25.3
26.5
3.2 . 46.71
3.5 . 55.44
24.0
55.57
6.0
19.5
10.7
47.18
21.1
3.0
51.20
28.0
1.4
30.8
48.91
1.4
31.15
58.7
4.0
20.05
55.3
0.5
13.79
75.3
0.0
11.11
81.8
0.3
12.22
74.7
1.3
14.89
57.6
63.1
1.0 . 14.03
0.1
14.83
59.7
0.7
13.22
68.3
0.1
15.88
73.4
11.58
0.0
78.9
5.0
47.60
34.2
31.48
50.5
5.3
1.4
48.38
33.4
56.25
47.50
42.50
42.50
51.25
46.25
62.50
32.50
21.25
20.00
20.00
17.50
17.50
40.00
58.75
72.50
62.50
63.75
42.50
48.75
43.75
48.75
46.25
53.75
47.50
37.50
28.75
22.50
17.50
12.50
17.50
12.50
12.50
10.00
23.75
17.50
17.50
47.40
42.50
47.50
15
15
14
13
8
11
8
20
27
30
27
27
29
19
14
11
11.
17
19
20
23
22
17
15
18
26
22
29
24
21
23
37
38
33
27
24
24
19
22
20
PKA
PQU
100
Table 35 (continued)
41
42
43
44
45
46
47
48
49
50
PSM
PIL
PVM
PCA
PKA
PQU
37.7
5.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
8.5
18.0
28.8
33.1
24.7
23.6
9.2
12.0
15.9
24.3
22.5
8.7
0.7
0.0
0.0
0.0
0.0
0.3
0.6
0.0
0.0
5.0
4.5
4.9
5.0
3.9
4.3
3.0
3.0
4.5
5.2
29.0
59.6
61.2
70.1
68.0
85.8
83.1
79.5
69.3
55.7
1.5
1.1
0.8
0.2
4.3
0.6
1.4
1.0
1.9
8.1
ECEC
LCEC
TKIL8
60.99
19.55 .
14.41
13.04
12.42
10.28
11.07
12.16
12.81
20.05
38.75
17.50
12.50
12.50
31.25
20.00
17.50
17.50
12.50
30.00
21
30
33
33
23
19
20
20
34
24
MONTANA STATE UNIVERSITY LIBRARIES
3 1762 00116369 8
N378
H778
c o p .2
DATE
Hopper, Roger W. E.
A sem i-q u a n tita tiv e
x -r a y d if f r a c t io n
technique fo r e s tim a tic
o f s m e c tite , i l l i t e , .
ISSUED
TO
$